GRB 191016A: A Long Gamma-Ray Burst Detected by TESS
Krista Lynne Smith, Ryan Ridden-Harper, Michael Fausnaugh, Tansu Daylan, Nicola Omodei, Judith Racusin, Zachary Weaver, Thomas Barclay, Péter Veres, D. Alexander Kann, Makoto Arimoto
DDraft version February 24, 2021
Preprint typeset using L A TEX style emulateapj v. 12/16/11
GRB 191016A: A LONG GAMMA-RAY BURST DETECTED BY TESS
Krista Lynne Smith , Ryan Ridden-Harper , Michael Fausnaugh , Tansu Daylan , Nicola Omodei , JudithRacusin , Zachary Weaver , Thomas Barclay , P´eter Veres , D. Alexander Kann , and Makoto Arimoto Draft version February 24, 2021
ABSTRACTThe TESS exoplanet-hunting mission detected the rising and decaying optical afterglow ofGRB 191016A, a long Gamma-Ray Burst (GRB) detected by
Swift -BAT but without prompt XRT orUVOT follow-up due to proximity to the moon. The afterglow has a late peak at least 1000 secondsafter the BAT trigger, with a brightest-detected TESS datapoint at 2589.7 s post-trigger. The burstwas not detected by
Fermi -LAT, but was detected by
Fermi -GBM without triggering, possibly due tothe gradual nature of rising light curve. Using ground-based photometry, we estimate a photometricredshift of z phot = 3 . ± .
40. Combined with the high-energy emission and optical peak time derivedfrom TESS, estimates of the bulk Lorentz factor Γ BL range from 90 − R = 15 . ∼ Keywords: galaxies:active - galaxies:nuclei - galaxies:Seyfert - radio:galaxies - stars:formation INTRODUCTION
The Transiting Exoplanet Survey Satellite, or TESS(Ricker et al. 2015), is currently in the midst of anearly all-sky timing survey in search of transiting plan-ets around M-dwarfs. On 2019 October 16 the BurstAlert Telescope (BAT; Barthelmy et al. 2005) onboardthe
Neil Gehrels Swift Observatory (Gehrels et al. 2004,
Swift hereafter) detected a gamma ray burst (GRB) inthe portion of the sky being monitored by TESS (Groppet al. 2019). The burst occurred too close to the moonfor
Swift to safely slew to its position, preventing UVOTand XRT follow-up until over 11 hours after the BATtrigger. The TESS data are therefore the only space-based follow-up for the burst before this time. Sev-eral ground-based observatories detected the counterpart KIPAC at SLAC, Stanford University, Menlo Park, CA 94025,USA; [email protected] Einstein Fellow Southern Methodist University, Department of Physics, Dallas,TX 75205, USA Research School of Astronomy & Astrophysics, Mount StromloObservatory, The Australian National University, Cotter Road,Weston Creek, ACT 2611, Australia MIT Kavli Institute for Astrophysics and Space Research, Mas-sachusetts Institute of Technology, Cambridge, MA, USA W. W. Hansen Experimental Physics Laboratory, Kavli In-stitute for Particle Astrophysics and Cosmology, Department ofPhysics and SLAC National Accelerator Laboratory, Stanford Uni-versity, Stanford, CA 94305, USA Astrophysics Science Division, NASA Goddard Space FlightCenter, Mail Code 661, Greenbelt, MD 20771, USA Institute for Astrophysical Research, Boston University, 725Commonwealth Avenue, Boston, MA, 02215 USA Exoplanets and Stellar Astrophysics Laboratory, Code 667,NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA University of Maryland, Baltimore County, 1000 Hilltop Cir-cle, Baltimore, MD 21250, USA Center for Space Plasma and Aeronomic Research, Universityof Alabama in Huntsville, Huntsville, AL 35899, USA Instituto de Astrof´ısica de Andaluc´ıa (IAA-CSIC), Glorietade la Astronom´ıa s/n, 18008 Granada, Spain Faculty of Mathematics and Physics, Institute of Science andEngineering, Kanazawa University, Kakuma, Kanazawa, Ishikawa920-1192, Japan and afterglow simultaneously with the TESS measure-ments, as documented in the GRB Coordinates Network(GCN) (Watson et al. 2019a,b; Zheng et al. 2019; Huet al. 2019; Kim et al. 2019; Schady & Bolmer 2019; Tomaet al. 2019).TESS clearly detects the rising pre-peak light curve ofthis long GRB. Here, we present the TESS light curveand discuss the viability of TESS data to help constrainproperties of GRBs that happen to occur within its fieldof view.In Section 2, we give the parameters of the burst asreported by Swift . In Section 3 we discuss the TESSmission and the extraction of the light curve. Section 4discusses the high energy emission from the burst as ob-served by
Fermi , while Section 5 presents the opticalafterglow properties and how they compare to knownbursts. Section 6 presents the photometric modelling todetermine the redshift of the afterglow. In Section 7, weuse the redshift and burst parameters to calculate thebulk Lorentz factor. Section 8 presents the calculationof how many bursts may be observable with TESS, andSection 9 provides a brief conclusive summary.When redshift is dealt with in this document, we haveassumed a cosmology with H = 69 . − Mpc − ,Ω M = 0 . Λ = 0 . GRB 191016A
The BAT trigger for GRB 191016A occurred at04:09:00.91 UT on 2019 October 16. The enhanced posi-tion was reported as RA=02:01:04.67, DEC=+24:30:35.3(J2000), corresponding to no cataloged galaxy. TheBAT light curve lasts for approximately 210 secondsafter the trigger, with a poorly-constrained T du-ration of 220 ±
180 s. The burst had a fluence of1.12 × − erg cm − in the energy range 15 −
350 keVregardless of whether the light curve is modelled as apower law with or without a cutoff; in both models thebest fitting power law photon index is Γ ph = 1 . ± . https://gcn.gsfc.nasa.gov/ a r X i v : . [ a s t r o - ph . H E ] F e b Smith et al. where the sign convention used is E − Γ ph .Due to the moon constraints of the Swift -XRT andUVOT telescopes, the satellite did not immediately slewto the position of the burst. This means that the XRTand UVOT light curves of the afterglow, typically si-multaneous with ground-based follow-up, are delayed byseveral hours. GRB 191016A was at 72 ◦ from the Fermi -Large Area Telescope (LAT, Atwood et al. 2009) bore-sight. The burst entered the
Fermi -LAT field of viewabout 4 ks after the
Swift -BAT trigger, but was not de-tected by LAT. Despite being in the field-of-view of the
Fermi
Gamma-ray Burst Monitor (GBM, Meegan et al.2009), it did not cause a trigger but was detected; seeSection 4 for details.The earliest follow-up of the burst was ground-based,beginning a few hundred seconds after the trigger, aschronicled in the GCN (for references, see the Intro-duction); the burst peaks at an apparent magnitude of R = 15 . THE TESS MISSION AND LIGHT CURVE
During the recently completed TESS primary missionphase, the spacecraft observed each 24 ×
96 degree sectorof the sky (over 2300 square degrees) continuously for27 days, recording integrations every 30-minutes, beforemoving on to the next sector. At high ecliptic latitudes,the sectors overlap, resulting in light curves with ex-tended durations. The bandpass is wide and monolithic,spanning the red-optical to the NIR ( ∼ − ∼ Kepler light curves for use on extragalac-tic targets; Smith 2019).The TESS satellite is optimized to efficiently search forexoplanet transit signals around more than 20,000 starssimultaneously. This mission is not designed for deep,high resolution studies of individual objects. The TESSangular resolution is extremely low, with pixels measur-ing 21 (cid:48)(cid:48) across, frequently resulting in a situation whereno photometric extraction aperture is possible that doesnot include incidental nearby sources. Extraction of thelight curve is thus dependent upon the source proper-ties desired, the sky environment of the source, and thelocation on the TESS detector. To ensure that any con-clusions we draw in our analysis are robust against differ-ent methods, we extract the light curve in three differentways, described in this section.
Light Curve Extractions: Simple BackgroundSubtraction
In this simplest method of systematics mitigation, webegin by requesting a cutout of the sky around the regionof interest using the online TESSCut tool (Brasseuret al. 2019); this produces a FITS file with photometricimages at every cadence during the monitored sector(s),with all of the information provided in the full FFIs (e.g.,quality flags and time/flux errors). The bulk of the ma-nipulation of the FITS files is accomplished with the As-troPy library (Astropy Collaboration et al. 2013, 2018).We then choose an extraction aperture, by eye, to maxi-mize the flux from the GRB afterglow while still avoidingnearby sources, as well as a nearby background region de-void of sources with the same pixel size as the extractionaperture. We perform aperture photometry from eachcadence that is not flagged for pointing instability by theTESS mission, from both the extraction and backgroundapertures. Finally, the background light curve is sub-tracted from the source light curve. The chosen sourceand background apertures and the resulting light curveare shown in the first row of Figure 1. Note that Figure 1shows the light curves in TESS instrumental units, as isusual for TESS photometric studies. There is currentlyno accepted method of converting TESS counts to a mag-nitude system. The light curve is presented again, in acontext comparative to other afterglows, in Section 5, inmore traditional units for GRBs, with an attempt at amagnitude conversion. Light Curve Extraction: Interpolated Background
For this method, we interpolate the TESS backgroundfrom sky pixels. We also utilise TESSCut (Brasseuret al. 2019) in conjunction with the Kepler/TESS re-duction packages from Lightkurve (Lightkurve Collabo-ration et al. 2018) for this method, to get a 50 ×
50 pixelTESS image of the region surrounding the GRB. To iden-tify which pixels are background pixels we simulate a50 ×
50 pixel TESS image, centered on the GRB, us-ing the Gaia source catalogue (Gaia Collaboration et al.2018). The Gaia sources are mapped onto the simulatedimage with the TESS WCS. We convert Gaia source mag-nitudes to TESS magnitudes via m T ESS = m Gaia − . .
44. We thenconvolve the Gaia sources with a model TESS PSF, us-ing methodology based on the
DAVE pipeline (Kostovet al. 2019). Finally, all pixels of the simulated imagewith counts less than a limit are selected as backgroundpixels. We interpolate the background signal from thebackground pixels to all pixels in the image. This methodof simulating the image allows for a clear determinationof which pixels are dominated by the background.Following background subtraction simple aperturephotometry is performed with a 2 × Light Curve Extraction: PSF-Fitting
Modeling the target flux via PSF yields an alternativemethod to extract the flux of the target in each time bin.Towards this purpose, we perform PSF photometry of thetarget given the TESS full frame image data. We employ https://mast.stsci.edu/tesscut/ ESS-Detected GRB 191016A F l u x ( e / s ) Simple Background Subtraction F l u x ( e / s ) Interpolated Background F l u x ( e / s ) PSF-Fitting
Figure 1.
Light curves (left) and extraction and background apertures (right) of GRB 191016A. The first row shows the light curvereduced with simple background subtraction as derived in Section 3.1, the second row shows the light curve derived using the interpolatedbackground estimation method described in Section 3.2, and the third row shows the light curve derived using the PSF-fitting methoddescribed in Section 3.3 (because the PSF is fitted at each cadence, no stable aperture exists). All light curves are normalized by subtractingthe median of the first 100 cadences of the sector (not plotted), well before the
Swift trigger, which is denoted by the vertical dashed lines. the Pixel Response Function (PRF) model constructedby the TESS mission. This takes into account the opticalPSF as well as the pointing jitter of the detector. Wethen use 13 ×
13 pixel PRF models that are upsampledby a factor 9. We interpolate the model up to the thirdorder in subpixel shifts and evaluate the model images ofthe target and nearby known point sources in the TESSInput Catalog (TIC, Stassun et al. 2018). Finally, usingthese point source models as templates, we perform linearregression to infer the fluxes of all sources in each timebin. Inclusion of the templates of the nearby sourcesenables marginalization over the neighbors and reducespotential flux contamination from nearby sources. Each light curve and extraction aperture is plotted inFigure 1. The light curve is clearly rising in the first datapoint following the BAT trigger, peaks at the subsequentpoint, and then declines. The afterglow falls below theTESS limiting magnitude as the light curve flattens out;note that the post-burst baseline may be higher thanthe pre-burst baseline due to an increase in the lunarscattered light. After the TESS limit is reached, ground-based follow-up is needed to explore the afterglow evo-lution at fainter magnitudes than V ∼
18 mag. In Fig-ure 2, we show the sky image from TESS in the cadencebefore the BAT trigger and at the TESS peak cadence,with contrast enhanced for easier visibility. The extrac-
Smith et al. tion aperture shown in Figure 1 encompasses the newafterglow source PSF as completely as possible withoutincluding the nearby targets. HIGH ENERGY EMISSION
In this section we discuss the gamma ray emission fromGRB 191016A. Although undetected by
Fermi -LAT, theburst was detected by both
Swift -BAT (the trigger) and
Fermi -GBM (no trigger). The BAT light curve is shownin Figure 3, obtained from the
Swift
Burst Analyser (Evans et al. 2010) with a S/N = 5 binning. The GBMlight curve is shown in Figure 4.High-energy emission from GRBs has been observedby Fermi -LAT up to >
10 ks post-trigger (Ajello et al.2019). We preform an unbinned likelihood analysis inthe time window between 3.9 ks and 5.4 ks, when theGRB was in the LAT FoV, in the energy range of 0 . − <
100 degrees. No significant emission athigh energy is detected. We compute a flux upper limit of1.6 × − photon cm − s − , corresponding to an energyflux upper limit of 1.2 × − erg cm − s − assuming aphoton index of Γ ph = 2, typical of LAT GRBs.Even though GRB 191016A was in its field of view,Fermi-GBM was not triggered. The GBM targetedsearch (Goldstein et al. 2019) is the most sensitive, co-herent search for GRB-like signals. During the automaticprocessing of external triggers in the GBM continuousdata, the targeted search found a significant signalconsistent in time, sky location and lightcurve morphol-ogy with GRB 191016A. The reason GRB 191016A didnot trigger GBM is likely an interplay between differenteffects: (1) a gradual rise in intensity for this burst (2)the timescale on which GBM calculates the backgroundrates to determine excess (3) variations in the gamma-ray background at the time of GRB 191016A due to theroutine slewing of the spacecraft.We performed standard spectral analysis using RMfit . We selected data from T − . T +58 . dN/dE ∝ E − Γ ph exp( − E (2 − Γ ph ) /E peak ). The photonindex Γ ph = 1 . ± .
07 and the energy where the νF ν spectrum peaks, E peak = 197 ±
22 keV. The flux in thistime interval is F = (1 . ± . × − erg s − cm − (10-1000 keV range). Using the method described in Bloomet al. (2001), we integrate the spectrum in the canoni-cal 1 keV -10 MeV range and perform the k-correctionto obtain the isotropic-equivalent energy in gamma rays.We calculate E γ, iso = (2 . ± . × erg. A LATE-PEAKING AFTERGLOW
The brightest point in the TESS light curve occursat 2589.7 s after the BAT trigger. This is significantly https://fermi.gsfc.nasa.gov/ssc/data/analysis/rmfit/ later than a typical long GRB in which the optical riseis observed; Oates et al. (2009) find that in their sampleof 27 UVOT afterglows, all light curves are decaying by500 s after trigger in the observer’s frame. Such a latepeak is not unprecedented, however; peak times of ∼ seconds are still within the tail of the distributionsreported by Ghirlanda et al. (2018) for 67 afterglows withobserved peaks.In Figure 5, we show the three TESS afterglow lightcurves as computed in Section 3 and the ground-basedGCN light curve, overlaid upon the large sample of op-tical afterglows of long GRBs from Kann et al. (2010).Although the TESS light curves are relatively bright, nei-ther their peak magnitudes nor late peaking time is farout of the ordinary. Kann et al. (2010) (their Figure7) also show some examples of afterglows that peak atsignificantly later times, including GRB 970508 whichpeaked after one day.A very important caveat is necessary when compar-ing the brightness of the TESS afterglow to others inthe plot, however: there is currently no accepted con-version from TESS counts (as shown in Figure 1) andany conventional magnitude system. This is primar-ily due to the monolithic and unusual TESS bandpass.In order to make a reasonable approximation, we haveused the statement in the TESS Instrument Handbook that 15,000 e − s − are generated by the cameras for astar of apparent magnitude m = 10. We have therebycalculated the “zero flux” of the TESS bandpass to be ∼ . × e − s − , via m = − . F/F ). This numberis roughly consistent with what is obtained by comparingthe TESS light curves to the ground-based light curves,although the points are not simultaneous. Due to theroughness of this approach, the vertical normalization ofthe light curves on Figure 5 should be assumed to havelarge uncertainties.Each of the TESS light curves yields a different tem-poral decay index α , where F ∝ t α : α = − . α = − . α = − . https://heasarc.gsfc.nasa.gov/docs/tess/documentation.html ESS-Detected GRB 191016A Figure 2.
TESS full-frame image in the cadence just before the BAT trigger (left) and at the peak flux of the burst (center). Theemergence of the afterglow is apparent in the center of the image, indicated by the white arrow. Contrast has been increased versus theright panel of Figure 1 in order to increase visibility. The right panel shows the same region of the sky, with a slightly different orientation,in the Digitized Sky Survey (DSS); a small inset of the TESS image is provided in the bottom left corner to demonstrate the change inorientation. − − − − − − O b s e r v ed f l u x den s i t y ( Jy ) BAT − XRT data for GRB 191016A10 − P ho t on I nde x Time since BAT trigger (s)
Figure 3.
The
Swift -BAT (black) and XRT (red) light curve forGRB 191016A, binned for S/N = 5. The evolution of the photonindex is shown in the lower panel. This figure was obtained fromthe
Swift
Burst Analyser (Evans et al. 2010). after which the flux rises rapidly to the peak data pointbefore steeply decaying; the ground-based light curvesdo not indicate such a flattening, but do not definitivelyrule it out, either. If this is the case, it resembles theUVOT light curve of GRB 100418A, which peaked verylate at approximately 50ks post-trigger, and was deter-mined to most likely arise from continuous injection ofenergy into the forward shock (Marshall et al. 2011), aswas the optical afterglow of GRB 060729 (Grupe et al.2007). Indeed, a recent re-analysis of GRB 100418A byde Ugarte Postigo et al. (2018) showed that the afterglowre-brightened rapidly during the first day after the trig-ger, beginning 2.4 h after the burst. Other late-peakingafterglows have been interpreted as due to an off-axisviewing angle, where the peak occurs once the beam haswidened sufficiently to include the line of sight, as inGRB 080710 ( t peak ∼ × s, Kr¨uhler et al. 2009)and GRB 081028 ( t peak ∼ × s, Margutti et al.2010). The lack of a detection of GRB 191016A by Fermi -LAT may also support the off-axis interpretationfor this burst; however, if the photometric redshift calcu-
300 200 100 0 100 200 300time [s] (from 2019-10-16 04:09:00 UTC)46004800500052005400560058006000 r a t e ( c o un t s / s ) Figure 4.
The summed
Fermi -GBM lightcurve from NaI detec-tors 7, 9, a and b. The energy range is 50 −
300 keV and thetemporal resolution is 4 s. The brown curve is the fitted polyno-mial background. lated below (Section 6), z phot = 3 .
29, is correct, a nonde-tection is perhaps to be expected, since only one GRB ata higher redshift has been detected by
Fermi -LAT (GRB080916C at z = 4 .
35, Abdo et al. 2009).Late-peaking or complex afterglows can also be theresult of a number of other physical scenarios, includingreverse or forward shocks due to interaction with the ISMor progenitor winds (Sari & Piran 1999; Kobayashi et al.2004), the peak frequency of the synchrotron emissionmoving through the observing band (Sari et al. 1998), ordestruction of surrounding dust by radiation as the burstproceeds (Fruchter et al. 2001); see Oates et al. (2009)for a nice summary of these effects in greater detail. ESTIMATING THE REDSHIFT
The only constraint placed on the redshift by theGamma-ray Coordinates Network (GCN) circulars was z <
4, established by the RATIR team (Watson et al.2019a).In order to determine a more precise redshift, we makeuse of the GCN-reported GROND photometry (Schady& Bolmer 2019), plotted in Figure 6. Since we lack
Smith et al. (cid:4)(cid:13)(cid:1)(cid:8) (cid:4)(cid:13)(cid:1)(cid:7) (cid:4)(cid:13)(cid:1)(cid:6) (cid:3)(cid:2)(cid:3)(cid:4) (cid:3)(cid:2)(cid:4) (cid:4) (cid:4)(cid:3) (cid:4)(cid:3)(cid:3)(cid:5)(cid:11)(cid:5)(cid:10)(cid:5)(cid:9)(cid:5)(cid:8)(cid:5)(cid:7)(cid:5)(cid:6)(cid:5)(cid:5)(cid:5)(cid:4)(cid:5)(cid:3)(cid:4)(cid:12)(cid:4)(cid:11)(cid:4)(cid:10)(cid:4)(cid:9)(cid:4)(cid:8)(cid:4)(cid:7)(cid:4)(cid:6)(cid:4)(cid:5)(cid:4)(cid:4)(cid:4)(cid:3)(cid:12)(cid:11)(cid:10)(cid:9)(cid:8) (cid:1) (cid:11)(cid:7)(cid:14)(cid:1) (cid:1) (cid:1)(cid:8)(cid:19)$(cid:19) (cid:1) (cid:11)(cid:7)(cid:14)(cid:1) (cid:1) (cid:1)(cid:18)!!(cid:23)"(cid:1)(cid:13)(cid:27)(cid:30)(cid:27)$ (cid:1) (cid:17)(cid:9)(cid:16)(cid:16)(cid:1)(cid:8)(cid:19)$(cid:19)(cid:4)(cid:1)(cid:15)(cid:16)(cid:10)(cid:5)(cid:10)(cid:27)$$(cid:27)(cid:31)(cid:25) (cid:1) (cid:17)(cid:9)(cid:16)(cid:16)(cid:1)(cid:8)(cid:19)$(cid:19)(cid:4)(cid:1)(cid:12)(cid:31)$(cid:23)"! (cid:29)(cid:19)$(cid:23)(cid:22)(cid:1)(cid:6)(cid:19)(cid:21)(cid:28)(cid:25)" %(cid:31)(cid:22) (cid:1) (cid:17)(cid:9)(cid:16)(cid:16)(cid:1)(cid:8)(cid:19)$(cid:19)(cid:4)(cid:1)(cid:16)(cid:27)(cid:30)!(cid:29)(cid:23)(cid:1)(cid:6)(cid:19)(cid:21)(cid:28)(cid:25)" %(cid:31)(cid:22)(cid:1)(cid:16)%(cid:20)$"(cid:19)(cid:21)$(cid:27) (cid:31) (cid:2) (cid:12) (cid:13)(cid:13) (cid:7)(cid:5) (cid:14) (cid:7) (cid:6) (cid:1) (cid:3) (cid:5) (cid:1) (cid:10) (cid:4) (cid:8)(cid:11) (cid:9) (cid:14) (cid:15)(cid:6) (cid:7) $(cid:1)(cid:2)(cid:22)(cid:19)’
Figure 5.
Optical afterglows of GRB 191016A from the threeTESS approaches (Section 3; c.f. Figure 1), shown in green, com-pared to the long GRB afterglow sample from Kann et al. (2010).Also shown is the ground-based R -band light curve from the GCN,in red. UVOT photometry, we do not have the fullest SED pos-sible to constrain the redshift. However, with a simplemodel, we can arrive at a much more precise estimatethan from the g − r color alone.We follow the prescription laid out in Kr¨uhler et al.(2011), which we describe briefly here, along with oursimplifications. We begin by assuming that the intrinsicshape of the SED is a power law: F ν ( λ ) = F λ β , where F is a normalization constant. This intrinsic power lawis then modified by extinction in the host galaxy, andby any neutral hydrogen in the intergalactic mediumalong the line of sight. Many GRB afterglows exhibitdamped Lyman- α (DLA) absorption associated with thehost galaxy, which must also be accounted for. The ef-fect of extinction from within the Milky Way is negligible:N HI , MW = 7 . × cm − (HI4PI Collaboration et al.2016). After these effects are accounted for, the observedspectrum can be modelled as F ν ( λ ) = D α ( z ) F λ β exp[ − τ dust ( z, A V ) − τ DLA ( z, N H )] . (1)This model includes four free parameters: the redshift z ,the intrinsic power law index β , the host galaxy extinc-tion A V , and the host column density of neutral hydro-gen, N H . D α ( z ) is the wavelength-averaged attenuation dueto line blanketing from intergalactic neutral hydrogen.This is a monotonically-increasing function with red-shift, which we model as in Madau (1995) (see theirFigure 2). The first optical depth term, τ dust , accountsfor the host galaxy’s own dust reddening. As describedby Kr¨uhler et al. (2011), most bright GRB afterglowsare well-modelled by a local reddening law ( A λ /A V as afunction of wavelength) based on the Small MagellanicCloud, as opposed to models based on the Large Magel- lanic Cloud and the Milky Way; we nonetheless attemptthe modelling using each of the three extinction laws, re-produced from Pei (1992); the lowest χ values are foundusing the SMC version. With the reddening law in hand,we then follow Li et al. (2018): τ dust = (1 / . A V η ( ν ),where η ( ν ) = A λ /A V .The second optical depth term accounts for neutralhydrogen within the host galaxy ( τ DLA ). This term iscalculated following Totani et al. (2006): τ DLA ( λ obs ) = N H σ α [ ν obs (1 + z )], where ν obs = c/λ obs , and σ α is theexact formula for the frequency dependence of the Ly α cross-section (e.g., Madau & Rees 2000).We fit Equation 1 to the SED, using the observed fluxesand mean wavelengths in each filter, with the defini-tions above using a Nelder-Mead minimization (Nelder& Mead 1965), allowing z , β , log N H , and A V to varyfreely. We find that the best-fit model is achieved with z phot = 3 . ± . β = 0 . ± .
02, log N H = 23 . ± . A V = − . ± .
12, which achieves a reduced χ = 4 .
1. The uncertainties in the fit parameters wereestimated by using the results of the Nelder-Mead fit asthe basis of a new least-squares fit, which generates acovariance matrix. The parameter errors are then thesquare root of the product of the diagonal of this matrixand the reduced chi-squared value of the least-squaresfit.These parameters are within observed distributions forGRB host galaxies as reported by Li et al. (2018). Thevalue for N H is quite high, but with a large uncertainty.Such values have been observed in other bursts, such asGRB 080607 ( z = 3 . z ∼
3; see Corre et al.(2018) for a discussion.The SED, GROND filters, and best-fitting model areshown in Figure 6, along with a few other models forcomparison. BULK LORENTZ FACTOR
If indeed one of the above scenarios causes the late-peaking afterglow and the the burst is on-axis, with apeak time corresponding to the start of the afterglowemission, one can derive the bulk Lorentz factor of theoutflowing material using the equation and normaliza-tions given by Molinari et al. (2007):Γ BL ( t peak ) = (cid:34) E γ (1 + z ) πnm p c ηt (cid:35) / ≈ (cid:34) E γ, (1 + z ) η . n t , (cid:35) / , (2)where E γ, is the isoptropic-equivalent energy releasedin gamma rays normalized to 10 erg, n is the particledensity of the surrounding medium in cm − , the normal-ized radiative efficiency η . is defined as η = 0 . η . , and t peak , = t peak / (100s).To calculate E γ , the isotropic-equivalent energy re-leased by the burst in gamma rays, we use the relationfrom Bloom et al. (2001): E iso = S πD l z k, (3)where S is the fluence, D l is the luminosity distanceand k is the cosmological k -correction factor, which is ESS-Detected GRB 191016A z phot = 3 .
29. Using this and the fluence reported by theBAT detection (1 . × − erg cm − ; see Section 2), wefind that E iso = 6 . × erg. This is consistent withthe most populous region of the observed range of E iso found in a sample of 92 long GRBs by Ghirlanda et al.(2009). It is slightly higher than the value of E iso foundin Section 4; this inconsistency likely results from thelonger observation time and smaller energy window for Swift (15 −
350 keV), and the fact that E peak is not con-strained by Swift observations. Extrapolating a powerlaw from
Swift’s energy range to the 1 keV-10 MeV withno cutoff naturally results in a larger E iso . We thereforehave two values of E iso that can be used in Equation 2for Lorentz factor calculation.In addition to E iso , Equation 2 requires an estimate of t peak to determine the bulk Lorentz factor Γ BL . We mayeither take the TESS peak at face-value and declare itthe true peak time, or use extrapolation to determine theearliest possible peak time. The time between the BATtrigger and the brightest data point in the TESS lightcurve is 2589.7 seconds. Of course, the brightest TESSpoint may not represent the actual peak time, especiallysince the TESS cadence is a relatively coarse 30 minutes.The light curve is clearly still rising at the previous TESSdata point, which occurs 786 s after the BAT trigger,providing a lower limit on t peak .Based on the fact that the observed peak is relativelylate, we may instead assume that the true peak occurredsomewhere between the observed peak and the previousstill-rising data point. Oates et al. (2009) calculated thebest-fitting power law index to their sample of opticalGRB afterglow light curves within the first 500 seconds, α < . The steepest rising light curve in that sample had α < = 0 . ± .
14. If we use this value and extrapolatefrom the rising data point at t = 786s, and then see wherethat rising power law intersects with the declining powerlaw between the observed peak and the following datapoint, the inferred peak time occurs at t = 1316s. Ourtwo estimates for t peak are therefore 2590s and 1316s.If we take the observed peak cadence at t = 2590s to bethe true peak and use the value of E iso from Equation 3,the result is Γ BL = 103. This is consistent with thecorrelation between Γ BL and E iso for long GRBs fromGhirlanda et al. (2018) for a homogeneous ISM. Usingthe value of E iso from Section 4, we obtain Γ BL = 90.If we instead take the extrapolated peak time, t =1316 s , and use the value of E iso from Equation 3, weobtain a Lorentz factor of Γ BL = 133. With E iso fromSection 4, we obtain Γ BL = 117.These values of Γ BL are consistent with the cumulativedistribution of bulk Lorentz factors in afterglows with anobserved t peak for models that assume a homogeneouscircumburst medium (Ghirlanda et al. 2018), except forΓ BL = 90, which is low compared to that distribution. TESS AND GAMMA RAY BURSTS
In this section, we discuss how the TESS bandpass,sensitivity, sampling pattern and cadence will affect de-tection rates of GRBs, and to what extent a detectionlike GRB 191016A can be expected in the future.The chief advantage TESS offers in studying opticalafterglows of GRBs is its continuous coverage indepen-dent of a trigger, potentially capturing GRB afterglows F r a c t i o n a l T r a n s m i ss i o n ( Å ) l o g F l u x D e n s i t y ( J y ) g' r' i' z' J H K Figure 6.
Spectral energy distribution from the GROND instru-ment at La Silla Observatory, the filter curves of which are shown.The best-fitting model corresponds to z phot = 3 .
29, and is shownin red. Other parameters are discussed in Section 6. Four othermodels are shown in pink, with identical parameters to the best-fitting model, but with redshifts 1, 2, 4, and 5 from top-left tobottom-right. serendipitously, with a much higher sampling cadencethan other timing surveys like the Zwicky Transient Fa-cility (ZTF) or the Rubin Observatory’s Legacy Surveyof Space and Time (LSST). This is advantageous in theinstance seen here, when observing constraints preventeda rapid slew by
Swift , providing supplemental photome-try to ground-based observations. It would be especiallyhelpful in the case that a GRB does not trigger
Swift -BAT, providing potentially the only optical follow-up insuch cases; for example, for bursts which are only de-tected by
Fermi -GBM.A major limitation of TESS for GRB follow-up isits much brighter limiting magnitude compared to mostground-based telescopes. The TESS bandpass, as dis-cussed in Section 3, is red-white monolithic, spanning600-1100 nm. As such, it does not quite correspondto the traditional “white” filters on ground based tele-scopes. TESS uses a self-defined quantity, the “TESSmagnitude,” to determine its sensitivity limits, as canbe seen in the TESS Instrument Handbook . Thephotometric precision per 30-minute integration of theTESS cameras falls to ∼
10% at apparent magnitudes of ∼
18 mag (Ricker et al. 2015), and this is only true if asource is isolated and on a well-behaved portion of theCCD uncontaminated by scattered light.With full frame images spaced every ten minutes, aswill be the case starting in TESS Cycle 3, the worst-casescenario is that the burst occurs quasi-simultaneouslywith a TESS cadence. In this case, the next cadencewill occur 10 minutes, or 600 seconds, later. This is af-ter all of the light curves in the Oates et al. (2009) havepassed their peak and begun to decay. The distributionof afterglow apparent magnitudes depends on the timeafter the burst and the morphological type of the lightcurve. Akerlof & Swan (2007) found that the distribu-tion of afterglow apparent magnitudes of
Swift -detectedGRBs peaked at R ∼ . https://heasarc.gsfc.nasa.gov/docs/tess/documentation.html Smith et al.
10 12 14 16 18 20 22 24 26 28 m apparent N u m b e r o f E v e n t s Wang+ 2013 t=100sWang+ 2013 t=1000sWang+ 2013 t=1hrRoming+ 2017 detectionRoming+ 2017 peakAkerlof & Swan 2007
Figure 7.
Histogram of apparent magnitudes, mostly in the R band but all in bands within the monolithic TESS filter. Bluecurves correspond to the distributions reported by Roming et al.(2017); black curves correspond to the distributions reported byWang et al. (2013); the grey histogram represents the distribu-tion from Akerlof & Swan (2007). The TESS magnitude at whichphotometric precision falls below 10% is shown by the red verticalline. ferentiated the observed afterglow population by post-burst time and light curve morphology, finding apparentmagnitude distributions peaking at R = 16 .
1, 17.3, and18.4 mag for 100 s, 1000 s, and 3600 s (1 hr) after theburst. Roming et al. (2017) report the UVOT magni-tudes of the first-observed data point and the afterglowpeak as 17.06 and 17.7 mag, respectively. We reproducethese populations in Figure 7, and overplot the TESS10% photometry limit.Based on these distributions, approximately 60% ofbursts have afterglows that are above the TESS limit-ing magnitude for at least one cadence. This is a roughestimate, since the TESS bandpass does not correspondexactly to any of the bandpasses used in the works above.While it would be preferable to know how many burstswill have at least two cadences detected by TESS, pre-cise calculations on this point are not useful, since 18 magis not a hard limiting magnitude, and under good condi-tions, fainter objects can be detected by TESS and underpoor conditions the limit is brighter.In the case of GRB 191016A, the peak apparent mag-nitude is R = 15 . v , typ-ical burst SEDs are brighter in the red/infrared, andso the probable detection fraction in the redder TESSbandpass is likely higher than 60%. Additionally, any influence of dust in the Milky Way, the host galaxy, andabsorbers in the intergalactic medium are diminished atredder wavelengths. Spread over six years, this meansthat an occurrence rate of GRBs bright enough for TESSdetection is about 33 per year. During a given sector,TESS is surveying approximately 2300 square degrees,or about 4% of the sky; thus, the likely rate of such aGRB occurring in the TESS field of view is 4% of 33,or about one per year. In order for TESS to observeit, it must remain above the limiting magnitude for longenough that the TESS 10-minute cadence will captureit. If we assume the very common temporal decay index α = − .
4, a burst peaking at m = 16 mag will decaybelow m = 18 mag in 26s. Bursts peaking at m = 15and 14 mag will decay below m = 18 mag in 138 and720 seconds respectively; meaning that in the worst casescenario of a burst occurring just before a TESS cadence,only afterglows with relatively bright ( <
14 mag) peakswill be captured. The range of temporal decay indices,however, assures us that approximately half of burstswill have flatter decays than this, remaining brighter forlonger. Given the uncertainties in the true limits of TESSdetection, along with the possibility of TESS capturingthe burst near to its peak and the positive effects of theredder TESS bandpass, a detection rate of one GRB af-terglow per year remains a reliable estimate, if perhapsslightly optimistic. It is consistent with the current de-tection rate.This discussion is valid only for GRBs powerful enoughto trigger
Swift , since the comparison samples in Figure 7are based on
Swift triggers, and with sufficient positionalaccuracy to localize to a TESS source. It is possible thatthe TESS-GRB detection rate may be slightly higher, if,for example, orphan afterglows are taken into account. CONCLUSION
We have analyzed the TESS light curve and ground-based photometry of GRB 191016A, a long GRB de-tected by
Swift -BAT. The afterglow has a late peak thatis at least 1000 seconds after the BAT trigger, with abrightest-detected TESS datapoint at 2589.7 s. Usingphotometric modelling, we have determined the redshiftof the afterglow to be z phot = 3 . ± .
40. The burstwas not immediately observed by the XRT and UVOTdue to its proximity to the moon, which is true of about14% of
Swift bursts; the serendipitous ongoing monitor-ing of TESS therefore provided prompt follow-up withina few minutes that otherwise would have been missed forthis burst, supplementing triggered ground-based obser-vations. Simple arithmetic arguments based on archivalafterglow samples imply that TESS will likely detect ∼ Swift triggers.Support for KLS was provided by the National Aero-nautics and Space Administration through Einstein Post-doctoral Fellowship Award Number PF7-180168, issuedby the Chandra X-ray Observatory Center, which is op-erated by the Smithsonian Astrophysical Observatoryfor and on behalf of the National Aeronautics SpaceAdministration under contract NAS8-03060. P.V. ac-knowledges support from NASA grants 80NSSC19K0595and NNM11AA01A. This paper includes data col-
ESS-Detected GRB 191016A
Gaia ( ),processed by the Gaia
Data Processing and Analy-sis Consortium (DPAC, ). Funding for theDPAC has been provided by national institutions, in par-ticular the institutions participating in the
Gaia