An extreme magneto-ionic environment associated with the fast radio burst source FRB 121102 D. Michilli 1,2,* , A. Seymour 3,* , J. W. T. Hessels 1,2,* , L. G. Spitler 4 , V. Gajjar 5,6,7 , A. M. Archibald 2,1 , G. C. Bower 8 , S. Chatterjee 9 , J. M. Cordes 9 , K. Gourdji 2 , G. H. Heald 10 , V. M. Kaspi 11 , C. J. Law 12 , C. Sobey 13,10 , E. A. K. Adams 1,14 , C. G. Bassa 1 , S. Bogdanov 15 , C. Brinkman 16 , P. Demorest 17 , F. Fernandez 3 , G. Hellbourg 12 , T. J. W. Lazio 18 , R. S. Lynch 19,20 , N. Maddox 1 , B. Marcote 21 , M. A. McLaughlin 22,20 , Z. Paragi 21 , S. M. Ransom 23 , P. Scholz 24 , A. P. V. Siemion 12,25,26 , S. P. Tendulkar 11 , P. Van Rooy 27 , R. S. Wharton 4 , D. Whitlow 3 Published online by Nature on 10 Jan 2018. DOI: 10.1038/nature25149 1 ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands 2 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands 3 National Astronomy and Ionosphere Center, Arecibo Observatory, PR 00612, USA 4 Max-Planck-Institut f ¨ ur Radioastronomie, Auf dem H ¨ ugel 69, D-53121 Bonn, Germany 5 Space Science Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94710, USA 6 Xinjiang Astronomical Observatory, CAS, 150 Science 1-Street, Urumqi, Xinjiang 830011, China 7 Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing 210008, China 8 Academia Sinica Institute of Astronomy and Astrophysics, 645 N. A’ohoku Place, Hilo, HI 96720, USA 9 Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University, Ithaca, NY 14853, USA 10 CSIRO Astronomy and Space Science, 26 Dick Perry Avenue, Kensington, WA 6151, Australia 11 Department of Physics and McGill Space Institute, McGill University, 3600 University, Montr´ eal, QC H3A 2T8, Canada 12 Department of Astronomy and Radio Astronomy Lab, University of California, Berkeley, CA 94720, USA 13 International Centre for Radio Astronomy Research - Curtin University, GPO Box U1987, Perth, WA 6845, Australia 14 Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AA, Groningen, The Netherlands 15 Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA 16 Physics Department, University of Vermont, Burlington, VT 05401, USA 17 National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801 USA 18 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA 19 Green Bank Observatory, PO Box 2, Green Bank, WV 24944, USA 20 Center for Gravitational Waves and Cosmology, Chestnut Ridge Research Building, Morgan- town, WV 26505, USA 21 Joint Institute for VLBI ERIC, Postbus 2, 7990 AA Dwingeloo, The Netherlands 1 arXiv:1801.03965v1 [astro-ph.HE] 11 Jan 2018
Transcript
An extreme magneto-ionic environment associated withthe fast radio burst source FRB 121102D. Michilli1,2,∗, A. Seymour3,∗, J. W. T. Hessels1,2,∗, L. G. Spitler4, V. Gajjar5,6,7, A. M. Archibald2,1,G. C. Bower8, S. Chatterjee9, J. M. Cordes9, K. Gourdji2, G. H. Heald10, V. M. Kaspi11, C. J. Law12,C. Sobey13,10, E. A. K. Adams1,14, C. G. Bassa1, S. Bogdanov15, C. Brinkman16, P. Demorest17,F. Fernandez3, G. Hellbourg12, T. J. W. Lazio18, R. S. Lynch19,20, N. Maddox1, B. Marcote21,M. A. McLaughlin22,20, Z. Paragi21, S. M. Ransom23, P. Scholz24, A. P. V. Siemion12,25,26, S. P. Tendulkar11,P. Van Rooy27, R. S. Wharton4, D. Whitlow3
Published online by Nature on 10 Jan 2018. DOI: 10.1038/nature25149
1ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, TheNetherlands2Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XHAmsterdam, The Netherlands3National Astronomy and Ionosphere Center, Arecibo Observatory, PR 00612, USA4Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany5Space Science Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94710, USA6Xinjiang Astronomical Observatory, CAS, 150 Science 1-Street, Urumqi, Xinjiang 830011, China7Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing 210008, China8Academia Sinica Institute of Astronomy and Astrophysics, 645 N. A’ohoku Place, Hilo, HI 96720,USA9Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, CornellUniversity, Ithaca, NY 14853, USA10CSIRO Astronomy and Space Science, 26 Dick Perry Avenue, Kensington, WA 6151, Australia11Department of Physics and McGill Space Institute, McGill University, 3600 University,Montreal, QC H3A 2T8, Canada12Department of Astronomy and Radio Astronomy Lab, University of California, Berkeley, CA94720, USA13International Centre for Radio Astronomy Research - Curtin University, GPO Box U1987, Perth,WA 6845, Australia14Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AA, Groningen,The Netherlands15Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA16Physics Department, University of Vermont, Burlington, VT 05401, USA17National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801 USA18Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA19Green Bank Observatory, PO Box 2, Green Bank, WV 24944, USA20Center for Gravitational Waves and Cosmology, Chestnut Ridge Research Building, Morgan-town, WV 26505, USA21Joint Institute for VLBI ERIC, Postbus 2, 7990 AA Dwingeloo, The Netherlands
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22Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA23National Radio Astronomy Observatory, Charlottesville, VA 22903, USA24National Research Council of Canada, Herzberg Astronomy and Astrophysics, Dominion RadioAstrophysical Observatory, P.O. Box 248, Penticton, BC V2A 6J9, Canada25Radboud University, Nijmegen, Comeniuslaan 4, 6525 HP Nijmegen, The Netherlands26SETI Institute, 189 N Bernardo Ave #200, Mountain View, CA 94043, USA27Department of Electrical Engineering and Computer Science, Case Western Reserve University,Cleveland, OH 44106, USA∗ These authors contributed equally to this work
Fast radio bursts (FRBs) are millisecond-duration, extragalactic radio flashes of unknownphysical origin1–3. FRB 121102, the only known repeating FRB source4–6, has been localizedto a star-forming region in a dwarf galaxy7–9 at redshift z = 0.193, and is spatially coincidentwith a compact, persistent radio source7, 10. The origin of the bursts, the nature of the per-sistent source, and the properties of the local environment are still debated. Here we presentbursts that show ∼100% linearly polarized emission at a very high and variable Faraday ro-tation measure in the source frame: RMsrc = +1.46 × 105 rad m−2 and +1.33 × 105 rad m−2at epochs separated by 7 months, in addition to narrow (. 30µs) temporal structure. Thelarge and variable rotation measure demonstrates that FRB 121102 is in an extreme and dy-namic magneto-ionic environment, while the short burst durations argue for a neutron starorigin. Such large rotation measures have, until now, only been observed11, 12 in the vicinitiesof massive black holes (MBH & 104 M�). Indeed, the properties of the persistent radio sourceare compatible with those of a low-luminosity, accreting massive black hole10. The burstsmay thus come from a neutron star in such an environment. However, the observed proper-ties may also be explainable in other models, such as a highly magnetized wind nebula13 orsupernova remnant14 surrounding a young neutron star.
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Using the 305-m William E. Gordon Telescope at the Arecibo Observatory, we detected 16bursts from FRB 121102 at radio frequencies from 4.1−4.9 GHz (Table 1). The data recorder pro-vided complete polarization parameters with 10.24-µs time resolution. See Methods and ExtendedData Figs. 1-6 for observation and analysis details.
The 4.5-GHz bursts have typical widths . 1 ms, which are narrower than the 2 to 9-ms burstspreviously detected at lower frequencies5, 15. In some cases they show multiple components andstructure close to the sampling time of the data. Burst #6 is particularly striking, with a widthof . 30µs, which constrains the size of the emitting region to . 10 km, modulo geometric andrelativistic effects. Evolution in burst morphology with frequency complicates the determination5
of dispersion measure (DM =∫ d
0ne(l) dl), but aligning the narrow component in Burst #6 results
in DM= 559.7 ± 0.1 pc cm−3, which is consistent4, 5, 15, 16 with other bursts detected since 2012,and suggests that any bona fide dispersion measure variations are at the . 1% level.
After correcting for Faraday rotation, and accounting for ∼2% depolarization from the finitechannel widths, the bursts are consistently ∼100% linearly polarized (Fig. 1). The polarizationangles PA = PA∞ + θ (where PA∞ is a reference angle at infinite frequency, θ = RMλ2 is therotation angle of the electric field vector and λ is the observing wavelength) are flat across theobserved frequency range and burst envelopes (∆PA . 5◦ms−1). This could mean that the burstdurations reflect the timescale of the emission process and not the rate of a rotating beam sweepingacross the line of sight. Any circular polarization is less than a few percent of the total intensity.Faraday rotation measure is defined RM = 0.81
∫ 0
dB‖(l) · ne(l) dl, where B‖ is the line-of-sight
magnetic field strength (µG), l is the distance (parsecs), and ne is the electron density (cm−3);by convention RM is positive when the magnetic field points toward the observer. On average,the observed RMobs = (+1.027 ± 0.001) × 105 rad m−2 and varies by ∼ 0.5% between Areciboobserving sessions spanning a month (Fig. 2; Table 1). The lack of polarization in previous burstdetections15, 16 at 1.1− 2.4 GHz is consistent with the relatively coarse frequency channels causingbandwidth depolarization and constrains |RMobs| & 104 rad m−2 at those epochs.
Confirmation of this extreme Faraday rotation comes from independent observations at 4–8 GHz with the 110-m Robert C. Byrd Green Bank Telescope (GBT), which yield RMobs =(+0.935± 0.001)× 105 rad m−2 at an epoch 7 months later than the Arecibo detections. The GBTand Arecibo RMobs differ with high statistical significance and indicate that the rotation measurecan vary by at least 10% on half-year timescales (Table 1 and Extended Data Fig. 5).
The Faraday rotation must come almost exclusively from within the host galaxy: the ex-pected Milky Way contribution17 is −25 ± 80 rad m−2, while estimated intergalactic mediumcontributions18 are . 102 rad m−2. In the source reference frame, RMsrc = RMobs × (1 + z)2 =+1.46× 105 rad m−2 and +1.33× 105 rad m−2 in the Arecibo and GBT data, respectively. The ob-served variations in rotation measure, without a correspondingly large change in dispersion mea-sure, imply that the Faraday rotation comes from a spatially compact region with a high magneticfield. Furthermore, that region must be close to FRB 121102, since it is extremely unlikely that theline of sight coincidentally encounters a small but un-associated structure with the required highmagnetic field.
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We can fit all 16 Arecibo bursts with a single PAglobal∞ = 58◦ ± 1◦ (referenced to infinite
frequency; measured counter-clockwise from North to East) and a single RMglobal per observationday (Table 1); however, we cannot rule out small changes in the rotation measure (. 50 rad m−2)and polarization angle (. 10◦) between bursts. The GBT data are in tension with a single PAglobal
∞ ,but this could be an instrumental difference or reflection of the higher observing frequency. Thenear constancy of polarization angle suggests that the burst emitter has a stable geometric orienta-tion with respect to the observer. The & 98% linear polarization fraction at a single RM constrainsturbulent scatter19 σRM < 25 rad m−2 and a linear gradient across the source ∆RM < 20 rad m−2,and there is no evidence for deviations from the wavelength-squared (λ2) scaling of the Faradayrotation effect. A Rotation Measure Synthesis and RMCLEAN analysis also implies a Faraday thinmedium (see Methods).
In the rest frame, the host galaxy contributes DMHost ∼ 70–270 pc cm−3 to the total disper-sion measure of the bursts8. Given RMsrc, this corresponds to an estimated line-of-sight magneticfieldBFRB
‖ = (0.6−2.4)×fDM mG. This is a lower limit range because the dispersion measure con-tribution specifically related to the observed rotation measure (i.e. DMRM) could be much smallerthan the total dispersion measure contribution of the host (DMHost, dominated by the star-formingregion), which we quantify by the scaling factor fDM = DMHost/DMRM ≥ 1. For comparison,typical magnetic field strengths within the interstellar medium of our Galaxy20 are only ∼5µG.
We can constrain the electron density (ne), electron temperature (Te), and length scale (LRM)of the region causing the Faraday rotation by balancing the magnetic field and thermal energydensities (Extended Data Fig. 6). For example, assuming equipartition and Te = 106 K, we find adensity of ne ∼ 102cm−3 on a length scale LRM ∼ 1 pc, i.e., comparable to the upper limit on thesize of the persistent source10.
A star-forming region, like that hosting FRB 121102, will contain HII regions of ionizedhydrogen. While ultracompact HII regions have sufficiently high magnetic fields and electrondensities to explain the large rotation measure, the constraints from DMHost and the absence offree-free absorption of the bursts exclude a wide range of HII region sizes and densities21 fortypical temperatures of 104 K.
The environment around a massive black hole is consistent with the (ne, LRM, Te) constraints22,and the properties of the persistent source are compatible with those of a low-luminosity, ac-creting massive black hole10. The high rotation measure toward the Galactic Centre magnetar23
PSR J1745−2900 (Fig. 3), RM = −7× 104 rad m−2, provides an intriguing observational analogyfor a scenario in which the bursts are produced by a neutron star in the immediate environment of amassive black hole. However, FRB 121102’s bursts are many orders of magnitude more energeticthan those of PSR J1745−2900 or any Galactic pulsar.
Alternatively, a millisecond magnetar model has previously been proposed8, 10, 13 for FRB 121102,and in that model one would expect a surrounding supernova remnant and nebula powered by thecentral neutron star. The (ne, LRM, Te) constraints are broadly compatible with the conditionsin pulsar wind nebulae, but dense filaments like those seen in the Crab Nebula24 may need to be
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invoked to explain the high and variable rotation measure of FRB 121102. In a young neutron starscenario, an expanding supernova remnant could also in principle produce a high rotation measureby sweeping up surrounding ambient medium and progenitor ejecta25.
A more detailed discussion of these scenarios is provided in the Methods, and more exoticmodels also remain possible26.
Regardless of its nature, FRB 121102 clearly inhabits an extreme magneto-ionic environ-ment. In contrast, Galactic pulsars with comparable dispersion measures have rotation measuresthat are less than a hundredth that of FRB 121102 (Fig. 3). FRB 121102’s RMsrc is also ∼500×larger than that detected in any FRB to date27. The five other known FRBs with polarimetricmeasurements present a heterogeneous picture, with a range of polarization fractions and rotationmeasures3. As also previously considered28, FRB 121102 suggests that FRBs with no detectablelinear polarization may actually have very large |RM| & 104 − 105 rad m−2 that was undetectablegiven the limited frequency resolution (0.4-MHz channels at 1.4 GHz) of the observations.
Monitoring of FRB 121102’s rotation measure and polarization angle with time, along withsearches for polarization and Faraday rotation from the persistent source, can help differentiateamong models. FRB 121102 is peculiar not only because of its large rotation measure but alsobecause it is the only known repeating FRB. While this may indicate that FRB 121102 is a funda-mentally different type of source compared to the rest of the FRB population, future measurementscan investigate a possible correlation between FRB repetition and rotation measure. Perhaps themarkedly higher activity level of FRB 121102 compared to other known FRBs is predominantlya consequence of its environment; e.g., because these magnetized structures can also boost thedetectability of the bursts via plasma lensing29.
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23. Eatough, R. P. et al. A strong magnetic field around the supermassive black hole at the centreof the Galaxy. Nature 501, 391–394 (2013).
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Acknowledgements We heartily thank the staff of both the Arecibo Observatory and Green Bank Obser-vatory for their continued support and dedication to enabling observations like those presented here. Wealso thank B. Adebahr, L. Connor, G. Desvignes, R. Eatough, R. Fender, M. Haverkorn, A. Karastergiou,R. Morganti, E. Petroff, F. Vieyro, and J. Weisberg for helpful suggestions and comments on the manuscript.The Arecibo Observatory is operated by SRI International under a cooperative agreement with the NationalScience Foundation (AST-1100968), and in alliance with Ana G. Mendez-Universidad Metropolitana, andthe Universities Space Research Association. The Green Bank Observatory is a facility of the NationalScience Foundation operated under cooperative agreement by Associated Universities, Inc. BreakthroughListen (BL) is managed by the Breakthrough Initiatives, sponsored by the Breakthrough Prize Foundation(www.breakthroughinitiatives.org). The research leading to these results has received funding from the Eu-ropean Research Council (ERC) under the European Union’s Seventh Framework Programme (FP7/2007-2013). J.W.T.H. is a Netherlands Organisation for Scientific Research (NWO) Vidi Fellow, and together withD.M., K.G. and C.G.B. also gratefully acknowledges funding for this work from ERC Starting Grant DRAG-NET under contract no. 337062. L.G.S. gratefully acknowledges financial support from the ERC StartingGrant BEACON, under contract number 279702, as well as the Max Planck Society. A.M.A. is an NWOVeni Fellow. S.C., J.M.C., P.D., T.J.L., M.A.M., and S.M.R. are partially supported by the NANOGravPhysics Frontiers Center (NSF award 1430284). V.M.K. holds the Lorne Trottier Chair in Astrophysics& Cosmology and a Canada Research Chair and receives support from an NSERC Discovery Grant andHerzberg Prize, from an R. Howard Webster Foundation Fellowship from the Canadian Institute for Ad-vanced Research (CIFAR), and from the FRQNT Centre de Recherche en Astrophysique du Quebec. C.J.L.acknowledges support from NSF award 1611606. Part of this research was carried out at the Jet PropulsionLaboratory, California Institute of Technology, under a contract with the National Aeronautics and SpaceAdministration. B.M. acknowledges support from the Spanish Ministerio de Economıa y Competitividad
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(MINECO) under grants AYA2016-76012-C3-1-P and MDM-2014-0369 of ICCUB (Unidad de Excelencia“Marıa de Maeztu”). S.M.R. is a CIFAR Senior Fellow. P.S. holds a Covington Fellowship at DRAO.
Author Contributions A.S. led development of the Arecibo observing functionality used here, and dis-covered the first ∼ 4.5GHz bursts. L.G.S. is PI of the Arecibo monitoring campaign. D.M. discovered therotation measure and analyzed the burst properties in detail. K.G. comprehensively searched all Arecibo∼4.5 GHz data sets for bursts. J.W.T.H. led the discussion of interpretation and writing of the manuscript.A.M.A. guided development of the RM fitting code. G.H.H. and C.S. performed the RM Synthesis anddeconvolution analysis. G.B., S.C., J.M.C., V.G., V.M.K., C.J.L, M.A.M. and D.M., also made significantcontributions to the writing of the manuscript and analysis. V.G. observed, searched and detected burstsfrom the GBT at 6.5 GHz as a part of the BL monitoring campaign of known FRBs. A.Si. is the PI of theBL project. C.B. helped with the polarization calibration of the test pulsar. G.H. wrote a code to splice rawvoltages across compute nodes. All other co-authors contributed significantly to the interpretation of theanalysis results and to the final version of the manuscript.
Competing Interests The authors declare that they have no competing financial interests.
Correspondence Correspondence and requests for materials should be addressed to J.W.T.H. (email:[email protected]).
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Table 1: Properties of Arecibo and GBT bursts. MJDs are referenced to infinite frequency at the solar systembarycentre; their uncertainties are of the order of the burst widths. Widths have uncertainties ∼ 10µs. Peak fluxdensities S and fluences F have ∼ 20% fractional uncertainties. RMs are not corrected for redshift and PAs arereferenced to infinite frequency. Bursts with no individual RM entry (–) were too weak to reliably fit on their own.The last two columns refer to a global fit of all bursts. All errors are 1σ; see Methods for observational details.
Figure 1 Polarization angles, pulse profile and spectrum of four bursts. A grey, horizontalline indicates the average PA of each burst. The red and blue lines indicate linear andcircular polarization profiles, respectively, while the black line is the total intensity. Burstnumbers are indicated next to the pulse profiles. Arecibo bursts (a and b) are plotted withtime and frequency resolutions of 10.24µs and 1.56 MHz, respectively. GBT bursts (c andd) are plotted with time and frequency resolutions of 10.24µs and 5.86 MHz, respectively.
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−1
0
1
Q/L
(a)
−1
0
1
U/L
(b)
4200 4300 4400 4500 4600 4700 4800
Frequency (MHz)
−25
0
25
∆PA
(deg
)
(c)
Figure 2 Faraday rotation in the bursts. a and b: variations of the Stokes Q and Uparameters with frequency, normalized by the total linear polarization (L =
√Q2 + U2),
for the six brightest Arecibo bursts detected on MJD 57747. Different bursts are plottedusing different colours. Only data points with S/N > 5 are plotted, and do not includeuncertainties. A black line represents the best-fit Faraday rotation model for the globalvalues reported in Table 1. c: difference between model and measured PA values with1-σ uncertainties around the central values indicated with black dots.
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101 102 103
DM (pc cm−3)
100
101
102
103
104
105
|RM|(
rad
m−
2)
PSR J1746-2849
PSR J1746-2856
PSR J1745-2900FRB 121102
FRB 110523
FRB 150215
FRB 150807
FRB 150418
Figure 3 Magnitude of rotation measure versus dispersion measure for FRBs and Galac-tic pulsars. Radio-loud magnetars are highlighted with red dots, while radio pulsars andmagnetars closest to the Galactic Centre are labelled by name (source: the ATNF PulsarCatalogue30). A green bar represents FRB 121102 and the uncertainty on the DM contri-bution of the host galaxy8. Green triangles are other FRBs with measured RM; here theDM is an upper limit on the contribution from the host galaxy.
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Methods
The analyses described here were based on the PRESTO31, PSRCHIVE32, and DSPSR33 pul-sar software suites, as well as custom-written Python scripts for linking utilities into reductionpipelines, fitting the data, and plotting.
Observations and burst search
Arecibo
We observed using the Arecibo ‘C-band’ receiver (dual linear receptors), in the frequencyrange 4.1 − 4.9 GHz, and the Puerto-Rican Ultimate Pulsar Processing Instrument (PUPPI) back-end recorder. The full list of observations is reported in Extended Data Table 1. We operatedPUPPI in its ‘coherent search’ mode, which produced 10.24µs samples and 512 × 1.56 MHz fre-quency channels, each coherently dedispersed to DM = 557.0 pc cm−3. Coherent dedispersionwithin each 1.56-MHz channel means that the intra-channel dispersive smearing is < 2µs evenif the burst DM is 10 pc cm−3 higher/lower than the fiducial value of 557.0 pc cm−3 used in thePUPPI recording. The raw PUPPI data also provide auto- and cross-correlations of the two lin-ear polarizations, which can be converted to Stokes I, Q, U, and V parameters in post-processing.Before each observation, both a test scan on a known pulsar (PSR B0525+21) and a noise-diodecalibration scan (for polarimetric calibration) were performed.
Dedispersed time series with DM = 461 − 661 pc cm−3, in trial steps of 1 pc cm−3, weresearched using PRESTO’s single pulse search.py, which applies a matched-filter tech-nique to look for bursts with durations between 81.92µs to 24576µs (for any putative burst thatonly has a single peak with width < 81.92µs, the sensitivity will be degraded by a factor of afew, at most). The resulting DM-time-S/N events were grouped into plausible astrophysical burstcandidates using a custom sifting algorithm and then a dynamic spectrum of each candidate wasplotted for human inspection and grading. We found 16 bursts of astrophysical origin, and usedthe DSPSR package to form full-resolution, full-polarization PSRCHIVE ‘archive’ format files foreach burst.
Green Bank Telescope
On August 26, 2017, we observed FRB 121102 using the GBT ‘C-band’ receiver (4−8 GHz,with dual linear receptors) as part of a program of monitoring known FRB positions. Observationswere conducted with the Breakthrough Listen Digital Backend34, which allowed recording of base-band voltage data across the entire nominal 4-GHz bandwidth of the selected receiver. Scans ofa noise-diode calibration, of the flux calibrator 3C161 and of the bright pulsar PSR B0329+54supplemented the observations.
In post-processing, a total intensity, low-resolution filterbank data product was searched
14
for bursts with DM= 500 − 600 pc cm−3, using trial DMs in steps of 0.1 pc cm−3 and a GPU-accelerated search package to perform the incoherent dedispersion35. We detected36 15 bursts withS/N > 10. Here we present the properties of just the two brightest GBT bursts in order to confirmthe large RM observed by Arecibo and to quantify its variation in time. A detailed analysis of allGBT detections is presented in Gajjar et al. (in prep.). A section of raw voltage data (1.5 s) aroundeach detected burst was extracted and coherently dedispersed to a nominal DM of 557.91 pc cm−3
using the DSPSR package. Final PSRFITS format data products have time and spectral resolutionsof 10.24µs and 183 kHz, respectively.
Data analysis
Calculation of burst RMs
We calibrated the burst ‘archives’ using the PSRCHIVE utility pac in ‘SingleAxis’ mode.This calibration strategy uses observations of a locally generated calibration signal (pulsed noisediode) to correct the relative gain and phase difference between the two polarization channels, un-der the assumption that the noise source emits equal power and has zero intrinsic phase differencein the two hands. This calibration scheme does not correct for cross-coupling or leakage betweenthe polarizations. While leakage must be present at some level, the high polarization fraction,complete lack of circular polarization, and consistency of the test pulsar observations with previ-ous work all give us confidence that calibration issues are not a significant source of error for theRM determination. In addition, the flux density of GBT observations was calibrated using the fluxcalibrator.
We initially performed a brute force search for peaks in the linear polarization fraction (Ex-tended Data Fig. 3), and discovered RMobs ∼ +105 rad m−2 in the Arecibo data. Each burst wascorrected for Faraday rotation using the best-fit RM value for that burst. Residual variations in theresulting PA(λ) were used to refine the initial values by fitting
PA(λ) = RMλ2 + PA∞. (1)
Subsequently, the equation
L = exp{i · 2(RMλ2 + PA∞)
}, (2)
where L is the unit vector of the linear polarization, was used to fit the whole sample of burststogether, imposing a different RM per day and a different PA∞ per telescope. The results of thesefits are reported in Table 1 and an example is shown in Fig. 2.
Applying the optimal RM value to each burst, we produced polarimetric profiles showingthat each burst is consistent with being ∼100% linearly polarized after accounting for the finitewidths of the PUPPI frequency channels (Fig. 1; Extended Data Fig. 2). In fact, the measured
15
Arecibo bursts are depolarized to ∼98%, consistent with an uncorrected intra-channel Faradayrotation of
∆θ =RMobsc
2∆ν
ν3c, (3)
where c is the speed of light, ∆ν is the channel width, and νc is the central channel observingfrequency. At 4.5 GHz this corresponds to ∼9◦, and the depolarization fraction is
fdepol = 1− sin(2∆θ)
2∆θ= 1.6%. (4)
We supplemented our above analysis with a combination of RM Synthesis and RMCLEAN(e.g. Extended Data Fig. 4). Ensuring the presence of minimal Faraday complexity is possible byintegrating across the full bandwidth and taking advantage of a Fourier transform relation betweenthe observed ~L(λ2) values and the Faraday spectrum (the polarized brightness as a function ofRM). This approach is commonly known as RM Synthesis37, and can be coupled with a deconvo-lution procedure (RMCLEAN) to estimate the intrinsic Faraday spectrum38. While RM Synthesisand RMCLEAN can have difficulty in properly reconstructing the intrinsic Faraday spectrum undercertain circumstances, the spread of clean components is a reliable indicator of spectra that containmore than a single Faraday-unresolved source39.
At each observed frequency, we integrated Stokes Q and U values across the pulse width andnormalized using Stokes I. Due to the normalization we only used frequency bins that had a StokesI signal-to-noise ratio of at least 5. We computed a deconvolved Faraday spectrum for each burstseparately, on a highly oversampled RM axis (δRM ≈ 10−4 of the nominal FWHM of the RMresolution element). We used a relatively small gain parameter (0.02) and terminated the decon-volution when the peak of the residual decreased to 2σ above the mean. The algorithm typicallyrequired 50 − 80 iterations to converge. This combination of settings permits us to carefully con-sider the cumulative distribution of RMCLEAN components along the RM axis, and thus constrainthe intrinsic width of the polarized emission to . 0.1% of the typical RM uncertainty. We foundthat this value scales with δRM because the peak of the Faraday spectrum rarely lands preciselyon an individual pixel. To a high degree of confidence, there is no evidence for emission at morethan one RM value, nor for a broadened (“Faraday thick”) emitting region; we therefore foregomore complicated QU-fitting19. Results of this analysis are shown in Extended Data Table 2, andare consistent with the simplified QU-fitting results described above.
Calculation of burst properties
As in previous studies5, 15, a search for periodicity in the burst arrival times remains incon-clusive.
Determining the exact DMs of the bursts is complicated by their changing morphology withradio frequency5, 15. Measuring DM based on maximizing the peak S/N of the burst often leadsto the blurring of burst structure and, in the case of FRB 121102, an overestimation of DM. We
16
have thus chosen to display all bursts dedispersed to the same nominal DM from Burst #6 (Fig. 1and Extended Data Fig. 1). Taking advantage of the narrowness of Burst #6, we estimated itsoptimal DM by minimizing its width at different DM trials. We measured burst widths at half themaximum by fitting von Mises functions using the PSRCHIVE routine paas (Table 1). Thesewidths correspond to the burst envelope in the case of multi-component bursts.
Flux densities of the Arecibo bursts were estimated using the radiometer equation to calculatethe equivalent RMS flux density of the noise:
σnoise =Tsys
G√
2Btint, (5)
where Tsys ∼ 30 K and G ∼ 7 K Jy−1 are the system temperature and gain of the receiver, re-spectively, B = 800 MHz is the observing bandwidth and tint = 10.24µs is the sampling time.GBT observations were instead calibrated using a flux calibrator as discussed above. Due to thecomplicated spectra of the bursts, we quote average values across the frequency band (Table 1).
The burst dynamic spectra in Extended Data Fig. 1 show narrow-band striations that areconsistent with diffractive interstellar scintillations caused by turbulent plasma in the Milky Way.Autocorrelation functions (ACFs) of burst spectra show three features: a very narrow feature fromradiometer noise, a narrow but resolved feature corresponding to the striations, and a broad featurerelated to the extent of the burst across the frequency band. The striation feature has a half widththat varies from ∼2 to 5 MHz from burst to burst and is comparable to the scintillation bandwidthexpected from the Milky Way in the direction of FRB 121102. The NE2001 electron densitymodel40 provides an estimate τ ∼ 16 µs for the pulse broadening at 1 GHz. This predicts ascintillation bandwidth ∼ ν4.4/2πτ that ranges from 5 to 11 MHz across the 4.1 to 4.9 GHz band.We conclude that the measured ACFs and the NE2001 model prediction are consistent to withintheir uncertainties and that the narrow striations are due to Galactic scintillations.
A model for FRB 121102’s rotation measure (RM) and scattering measure (SM)
RM constraints
The measured RMobs ∼ +1× 105 rad m−2 implies a source frame value
RMsrc = (1 + z)2RMobs ∼ +1.4× 105 rad m−2. (6)
We can use the previously estimated8 DMHost ∼ 70–270 pc cm−3 (in the source frame) andRMsrc to constrain the properties of the region in which the Faraday rotation occurs. In the absenceof other information, we can set a constraint on the average magnetic field along the line of sightin the Faraday region with the ratio
B‖ =RMsrc
0.81DMHost
= [0.6 mG, 2.4 mG]. (7)
17
If only a small portion of FRB 121102’s total DM is from the highly magnetized region, thefield could be much higher.
SM constraints
The best constraint on pulse broadening comes from the measurement of the scintillation(diffraction) bandwidth of ∆νd ∼ 5 MHz at 4.5 GHz (see above). This implies a pulse broadeningtime at 1 GHz:
This scattering time is consistent with that expected from the Milky Way using the NE2001 model40
and therefore is an upper bound on any contribution from the host galaxy. Compared to scatteringin the Milky Way, this upper bound is below the mean trend for any of the plausible values ofDMHost, especially when the correction from spherical to plane waves is taken into account41.
The ratio host-galaxy τ/DM is a factor (1 + z)2 = 1.42 larger in the source frame but thatis still far from sufficient to account for the apparent scattering deficit compared to the Galacticτ -DM relation. Given the apparent extreme conditions of the plasma in the host galaxy, it wouldnot be surprising if its turbulence properties cause a scattering deficit. For example, scatteringis reduced if the inner scale is comparable or larger than the Fresnel scale, either due to a largemagnetic field or a high temperature.
Constraints on the properties of the Faraday region
Comparison of the magnetic field and thermal energy densities enables us to constrain the density(ne), electron temperature (Te), and length scale (LRM) of the region responsible for the observedFaraday rotation. We parametrize this relation with
βB2
8π= 2nekBTe, (9)
where β is a scaling factor,B is the magnetic field strength, and kB is the Boltzmann constant. Thisassumes a 100% ionized gas of pure hydrogen with temperature equilibration between protons andelectrons. Under equipartition, β = 1. In more densely magnetized regions, β � 1. Field reversalswill reduce the total RM, requiring a lower value of β in order to match constraints. The absenceof free-free absorption at a frequency of ∼1 GHz sets an additional constraint on the permittedparameter space.
In Extended Data Fig. 6, we explore a range of physical environments. We consider a smallerlower limit, i.e. DM = 1 pc cm−3, on the dispersion measure than the previously estimated8
DMHost ∼ 70–270 pc cm−3, because not all of the DM may originate from the Faraday region.Galactic HII regions typically show |RM| . 3 × 102 rad m−2 and weak magnetic fields42 withβ & 1, although calculations suggest it is possible for HII regions to achieve high RMs under
18
some circumstances43. Parameter space for typical HII region plasma at Te = 104 K is almostentirely excluded, and considering a range of possible HII regions sizes and densities21 shows thatthese are incompatible with the DMHost constraints. At higher Te, wide ranges of parameter spaceare permitted. In the case of equipartition, we have explicit unique solutions. For Te = 106 K,we find a density of ne ∼ 102 cm−3 on a length scale LRM ∼ 1 pc, i.e., comparable to the upperlimit on the size of the persistent source. Higher temperature gas (Te = 108 K) can be extended toLRM ∼ 100 pc. For both of these solutions, the characteristic magnetic field strength is ∼1 mG.
The large RM of FRB 121102 is similar to those seen toward massive black holes; notably,RM ∼ −5 × 105 rad m−2 is measured toward Sgr A*, the Milky Way’s central black hole, andprobes scales of < 104 Schwarzschild radii (∼0.001 pc)11, 12. The constraints on ne, Te, and LRM
are also consistent with the environment around Sgr A* (Extended Data Fig. 6). The high RMtoward the Galactic Centre magnetar PSR J1745−2900 (Fig. 3), RM = −7 × 104 rad m−2, at aprojected distance of ∼0.1 pc from Sgr A* 23, 44, is evidence for a dynamically organized magneticfield around Sgr A* that extends out to the magnetar’s distance23. Notably, ∼4.5 years of radiomonitoring of PSR J1745−2900 has shown a∼5% decrease in the magnitude of the observed RM,while the DM remained constant at the ∼1% level (Desvignes et al., in prep.). This suggests largefluctuations in magnetic field strength in the Galactic Centre, on scales of roughly 10−5 parsec.
The high RM and the rich variety of other phenomena4, 5, 7–10, 15, 16 displayed by the FRB 121102system suggest that the persistent radio counterpart to FRB 121102 could represent emission froman accreting massive black hole, with the surrounding star formation representing a circum-black-hole starburst. Given the mass of the host galaxy, and typical scaling relationships45, the mass ofthe black hole would be ∼104−6 M�. The observed radio brightness, compactness, and the currentoptical and X-ray non-detections8, 10, 16 are compatible with such a black hole and an inefficientaccretion state (∼10−6–10−4 LEdd, where LEdd is the Eddington luminosity).
While models considering the presence of only a massive black hole have been proposed46,there is no observational precedent for microsecond bursts created in such environments. Rather,the FRB 121102 bursts themselves could arise from a neutron star, perhaps highly magnetized andrapidly spinning, near an accreting massive black hole. The proximity of PSR J1745−2900 to SgrA* demonstrates that such a combination is possible. In this model, the black hole is responsiblefor the observed persistent source, whereas the bursts are created in the magnetosphere of thenearby neutron star47.
Alternatively, the association of FRB 121102 with a persistent radio source has been usedto argue that the radio bursts are produced by a young magnetar powering a luminous windnebula13, 48. This model is not well motivated by Galactic examples, since the most luminous(non-magnetar powered) Galactic pulsar wind nebula is only 2 × 10−6 times as luminous as thepersistent source coincident with FRB 121102, and Galactic magnetars have no detectable per-sistent radio wind nebulae49, 50. Also, while giant flares from magnetars can produce relativisticoutflows51, an upper limit on the RM from one such outburst52 is 4 orders of magnitude below thatobserved for FRB 121102.
19
Nonetheless, under the millisecond magnetar model, the properties of the persistent sourceconstrain the putative magnetar’s age to be between several years and several decades with a spin-down luminosity of 108 to 1012 times higher than any local analog13. Furthermore, the millisecondmagnetar model predicts that the nebula magnetic field strength scales with the integrated spin-down luminosity of the magnetar13, 48. Extended Data Fig. 6 describes a range of sizes, densities,and temperatures for the Faraday-rotating medium that are consistent with Crab-like pulsar windnebulae, known supernova remnants, and a simple model for swept-up supernova ejecta.
Data availability
The calibrated burst data are available, upon request, from the Corresponding Author.
Code availability
The code used to analyse the data is available at the following sites:PRESTO (https://github.com/scottransom/presto),PSRCHIVE (http://psrchive.sourceforge.net),DSPSR (http://dspsr.sourceforge.net).
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32. van Straten, W., Demorest, P. & Oslowski, S. Pulsar Data Analysis with PSRCHIVE. Astro-nomical Research and Technology 9, 237–256 (2012).
33. van Straten, W. & Bailes, M. DSPSR: Digital Signal Processing Software for Pulsar Astron-omy Pubs. Astron. Soc. Australia 28, 1–14 (2011).
34. MacMahon, D. H. E. et al. The Breakthrough Listen Search for Intelligent Life: A WidebandData Recorder System for the Robert C. Byrd Green Bank Telescope. ArXiv e-prints (2017).1707.06024.
35. Barsdell, B. R., Bailes, M., Barnes, D. G. & Fluke, C. J. Accelerating incoherent dedispersion422, 379–392 (2012).
36. Gajjar, V. et al. FRB 121102: Detection at 4 - 8 GHz band with Breakthrough Listen backendat Green Bank. The Astronomer’s Telegram 10675 (2017).
37. Brentjens, M. A. & de Bruyn, A. G. Faraday rotation measure synthesis. Astron. Astrophys.441, 1217–1228 (2005).
38. Heald, G., Braun, R. & Edmonds, R. The Westerbork SINGS survey. II Polarization, Faradayrotation, and magnetic fields. Astron. Astrophys. 503, 409–435 (2009).
39. Anderson, C. S., Gaensler, B. M., Feain, I. J. & Franzen, T. M. O. Broadband Radio Po-larimetry and Faraday Rotation of 563 Extragalactic Radio Sources. Astrophys. J. 815, 49(2015).
40. Cordes, J. M. & Lazio, T. J. W. NE2001.I. A New Model for the Galactic Distribution of FreeElectrons and its Fluctuations. Preprint at http://arxiv.org/abs/astro-ph/0207156 (2002).
41. Cordes, J. M., Wharton, R. S., Spitler, L. G., Chatterjee, S. & Wasserman, I. Radio WavePropagation and the Provenance of Fast Radio Bursts. ArXiv e-prints (2016). 1605.05890.
42. Harvey-Smith, L., Madsen, G. J. & Gaensler, B. M. Magnetic Fields in Large-diameter H IIRegions Revealed by the Faraday Rotation of Compact Extragalactic Radio Sources. Astro-phys. J. 736, 83 (2011).
43. Sicheneder, E. & Dexter, J. A single H II region model of the strong interstellar scatteringtowards Sgr A*. Mon. Not. R. Astron. Soc. 467, 3642–3647 (2017).
44. Shannon, R. M. & Johnston, S. Radio properties of the magnetar near Sagittarius A* fromobservations with the Australia Telescope Compact Array. Mon. Not. R. Astron. Soc. 435,L29–L32 (2013).
45. Reines, A. E. & Volonteri, M. Relations between Central Black Hole Mass and Total GalaxyStellar Mass in the Local Universe. Astrophys. J. 813, 82 (2015).
46. Vieyro, F. L., Romero, G. E., Bosch-Ramon, V., Marcote, B. & del Valle, M. V. A model forthe repeating FRB 121102 in the AGN scenario. Astron. Astrophys. 602, A64 (2017).
47. Pen, U.-L. & Connor, L. Local Circumnuclear Magnetar Solution to Extragalactic Fast RadioBursts. Astrophys. J. 807, 179 (2015).
48. Kashiyama, K. & Murase, K. Testing the Young Neutron Star Scenario with Persistent RadioEmission Associated with FRB 121102. Astrophys. J. 839, L3 (2017).
49. Hester, J. J. The Crab Nebula: An Astrophysical Chimera. Ann. Rev. Astron. Astrophys. 46,127–155 (2008).
50. Reynolds, S. P. et al. Pulsar-Wind Nebulae and Magnetar Outflows: Observations at Radio,X-Ray, and Gamma-Ray Wavelengths. Space Science Reviews 207, 175–234 (2017).
51. Frail, D. A., Kulkarni, S. R. & Bloom, J. S. An outburst of relativistic particles from the softγ-ray repeater SGR1900+14. Nature 398, 127–129 (1999).
52. Gaensler, B. M. et al. An expanding radio nebula produced by a giant flare from the magnetarSGR 1806-20. Nature 434, 1104–1106 (2005).
53. McKee, C. F. & Truelove, J. K. Explosions in the interstellar medium. PhysRep 256, 157–172(1995).
54. Orlando, S., Miceli, M., Pumo, M. L. & Bocchino, F. Modeling SNR Cassiopeia A from theSupernova Explosion to its Current Age: The Role of Post-explosion Anisotropies of Ejecta.Astrophys. J. 822, 22 (2016).
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Extended Data
Extended Data Table 1: List of ∼4.5 GHz Arecibo observations used in this study. These are asubset of all FRB 121102 observations to date.
Extended Data Table 2: Results of RM Synthesis and RMCLEAN. RMs were determined by fittinga quadratic function to the peak of the deconvolved Faraday spectrum. RM uncertainties weredetermined by dividing the nominal FWHM of the RM resolution element by twice the signal-to-noise ratio at the peak of the RM spectrum. RMdisp is the second moment (dispersion) of theRMCLEAN clean components discovered during the Faraday spectrum deconvolution. Upper limitsindicate that the value scales with RM pixel size. A value of zero means that all clean componentsfell within the same pixel, and indicates a Faraday spectrum that is indistinguishable from beinginfinitely thin.
Extended Data Figure 1: Pulse profiles and spectra of the 16 Arecibo bursts. The bursts arede-dispersed to DM = 559.7 pc cm−3 (which minimizes the width of Burst #6) and plotted withtime and frequency resolutions of 20.48µs and 6.24 MHz, respectively.
Extended Data Figure 2: Polarimetric properties of the 11 brightest bursts detected by Arecibo.a: linear polarization fraction of the bursts as a function of frequency. A solid line shows the theo-retical depolarization due to intra-channel Faraday rotation calculated using Eqs. 3 and 4. b: PA∞as a function of frequency. For both panels, values are averaged over 16 consecutive channels. c:PA∞ as a function of time. A time offset is applied to each burst in order to show them consec-utively. Vertical, dashed lines divide different observing sessions. All values in this figure havebeen corrected for the RM calculated with a global fit. Grey regions in b and c indicate the 1-σuncertainty around the PA value from the global fit.
Extended Data Figure 3: Linear polarization fraction of the bursts as a function of RM. Differ-ent colours represent different observing sessions (see legend). A grey line indicates the averageRM yielding the largest polarization fraction in the first observing session.
Extended Data Figure 4: Example RM Synthesis and RMCLEAN for Burst #8. The relevantRM range is shown for Burst #8, after RM Synthesis (dashed line) and RMCLEAN (solid line), asdescribed in the text. Only two clean components (red circles) were required to reach convergencein the deconvolution algorithm (at 102, 679.5 and 102, 679.75 rad m−2; cf. the peak of the finaldeconvolved Faraday spectrum at 102, 679.65 rad m−2). For all bursts, the RM Synthesis andRMCLEAN steps demonstrate an extremely thin and single-peaked Faraday spectrum.
Extended Data Figure 5: RM and PA∞ values of the different bursts. Coloured, 1-σ error barsrepresent individual bursts, with central values highlighted by black dots. Horizontal grey regionsare values obtained from a global fit. Values used in the figure are reported in Table 1.
23
Extended Data Figure 6: Physical constraints from source parameters. Parameter space forelectron density (ne) and length scale (LRM) of the Faraday region for three different temperatureregimes, Te = [104, 106, 108] K. The shaded red region indicates parameter space excluded byoptical depth considerations (τff > 5). The solid black line gives the maximum DMHost permitted,while the shaded grey region shows the DM down to 1 pc cm−3. The solid blue line gives RMsrc.The shaded blue region gives the range 10−4 <= β <= 1. The intersection of grey and blueregions outside of the red region are physically permitted. The arrows indicates the upper limitson the sizes of the persistent source (left) and the star-forming region (right), respectively8, 10. Theparallel dashed lines represent fits to a range of galactic and extragalactic HII regions21. Theparallel dotted lines represent the evolution of 1 and 10 M� of ejecta evolving up to 1000 years ata velocity of 104 km s−1 in the blast-wave phase following a supernova53. The filled downwardstriangle and diamond are for the supernova remnants Cas A54 and SN 1987A55, respectively. Thefilled circle represents the mean density and diameter of the Crab Nebula, whereas the filled squarerepresents the characteristic density and length scale of a dense filament in the Crab Nebula24. Thestar indicates the density at the Bondi radius of Sgr A*22.
24
Extended Data Table 1: List of ∼4.5 GHz Arecibo observations used in this study. These are asubset of all FRB 121102 observations to date.
Start Duration # bursts
(M J D) (s)
57717.2018171 4146 0
57717.2500000 2378 0
57747.1172685 6703 10
57748.1141435 6806 5
57772.0590625 5901 1
57806.9996759 2700 0
57813.9342940 5588 0
57821.9134144 2893 0
57858.8624769 2350 0
57865.8491782 1904 0
57872.8160417 2919 0
57900.7106597 2779 0
25
Extended Data Table 2: Results of RM Synthesis and RMCLEAN. RMs were determined by fittinga quadratic function to the peak of the deconvolved Faraday spectrum. RM uncertainties weredetermined by dividing the nominal FWHM of the RM resolution element by twice the signal-to-noise ratio at the peak of the RM spectrum. RMdisp is the second moment (dispersion) of theRMCLEAN clean components discovered during the Faraday spectrum deconvolution. Upper limitsindicate that the value scales with RM pixel size. A value of zero means that all clean componentsfell within the same pixel, and indicates a Faraday spectrum that is indistinguishable from beinginfinitely thin.
Figure 1 Pulse profiles and spectra of the 16 Arecibo bursts. The bursts are de-dispersedto DM = 559.7 pc cm−3 (which minimizes the width of Burst #6) and plotted with time andfrequency resolutions of 20.48µs and 6.24 MHz, respectively.
Figure 2 Polarimetric properties of the 11 brightest bursts detected by Arecibo. a: linearpolarization fraction of the bursts as a function of frequency. A solid line shows the theo-retical depolarization due to intra-channel Faraday rotation calculated using Eqs. 3 and 4.b: PA∞ as a function of frequency. For both panels, values are averaged over 16 consecu-tive channels. c: PA∞ as a function of time. A time offset is applied to each burst in orderto show them consecutively. Vertical, dashed lines divide different observing sessions.All values in this figure have been corrected for the RM calculated with a global fit. Greyregions in b and c indicate the 1-σ uncertainty around the PA value from the global fit.
Figure 3 Linear polarization fraction of the bursts as a function of RM. Different coloursrepresent different observing sessions (see legend). A grey line indicates the average RMyielding the largest polarization fraction in the first observing session.
Figure 4 Example RM Synthesis and RMCLEAN for Burst #8. The relevant RM rangeis shown for Burst #8, after RM Synthesis (dashed line) and RMCLEAN (solid line), asdescribed in the text. Only two clean components (red circles) were required to reachconvergence in the deconvolution algorithm (at 102, 679.5 and 102, 679.75 rad m−2; cf. thepeak of the final deconvolved Faraday spectrum at 102, 679.65 rad m−2). For all bursts,the RM Synthesis and RMCLEAN steps demonstrate an extremely thin and single-peakedFaraday spectrum.
Figure 5 RM and PA∞ values of the different bursts. Coloured, 1-σ error bars representindividual bursts, with central values highlighted by black dots. Horizontal grey regionsare values obtained from a global fit. Values used in the figure are reported in Table 1.
32
Figure 6 Physical constraints from source parameters. Parameter space for electron den-sity (ne) and length scale (LRM) of the Faraday region for three different temperatureregimes, Te = [104, 106, 108] K. The shaded red region indicates parameter space ex-cluded by optical depth considerations (τff > 5). The solid black line gives the maximumDMHost permitted, while the shaded grey region shows the DM down to 1 pc cm−3. Thesolid blue line gives RMsrc. The shaded blue region gives the range 10−4 <= β <= 1. Theintersection of grey and blue regions outside of the red region are physically permitted.The arrows indicates the upper limits on the sizes of the persistent source (left) and thestar-forming region (right), respectively8,10. The parallel dashed lines represent fits to arange of galactic and extragalactic HII regions21. The parallel dotted lines represent theevolution of 1 and 10 M� of ejecta evolving up to 1000 years at a velocity of 104 km s−1
in the blast-wave phase following a supernova53. The filled downwards triangle and dia-mond are for the supernova remnants Cas A54 and SN 1987A55, respectively. The filledcircle represents the mean density and diameter of the Crab Nebula, whereas the filledsquare represents the characteristic density and length scale of a dense filament in theCrab Nebula24. The star indicates the density at the Bondi radius of Sgr A*22.
