Multi-messenger light curves from gamma-ray bursts 1409.2874, 1606.02325 Mauricio Bustamante Center for Cosmology and AstroParticle Physics (CCAPP) The Ohio State University 8th Huntsville Gamma-Ray Burst Symposium Huntstville October 24, 2016 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 1
Why are GRBs natural ν source candidates? 1 They are bright 10 52 10 53 erg in gamma rays (Sun: 10 40 erg in 1 yr; SN: 10 42 erg) Photons up to 100 GeV Implies possible acceleration of protons to high energies 2 They have fast time-variability Features at 0.01 s scale Compact emission regions Implies high proton and photon number densities (pγ ν) Natural expectation: GRBs produce copious high-energy neutrinos (But they are far and relatively rare) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 2
Our expectations, unrewarded? IceCube has not found neutrinos associated to GRBs 3 yr of showers (all flavors) + 4 yr of upgoing tracks with > 1 TeV Catalog of 807 bursts 6 coincident events (5 showers + 1 track) not statistically significant 1% of the diffuse flux can be from prompt GRB emission ICECUBE, ApJ 824, 115 (2016) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 3
The elephant in the room Why is it still interesting to look for GRB neutrinos? 1 Best candidates for joint high-energy e.m. neutrino emission 2 Potential sources of ultra-high-energy cosmic rays Also... 3 Choked bursts might contribute sizeably to the diffuse flux e.g., [P. MÉSZAROS, E. WAXMAN 2001] [N. SENNO, K. MURASE, P. MÉSZAROS 2016] [I. TAMBORRA, S. ANDO 2016] 4 Neutrinos from GRB afterglows expected at EeV e.g., [K. MURASE 2007] [S. RAZZAQUE, L. YANG 2015] So, every bit of insight into how GRBs make neutrinos is essential Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 4
GRBs a zoo of light curves Photon rate (10 2 counts s 1 ) BATSE variability timescale (width of pulses) t v 0.01 s Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 5
Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 GRB920513 Trigger 1606 Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 GRB931008 Trigger 2571 5 0 20 40 60 80 100 Time since trigger [s] 10 0 20 40 60 80 100 Time since trigger [s] can we tell which GRB is likely bright in neutrinos? Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6
Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 5 GRB920513 Trigger 1606 0 20 40 60 80 100 Time since trigger [s] Fast time variability can we tell which GRB is likely bright in neutrinos? Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 GRB931008 Trigger 2571 0 20 40 60 80 100 Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6
Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 5 GRB920513 Trigger 1606 0 20 40 60 80 100 Time since trigger [s] Fast time variability can we tell which GRB is likely bright in neutrinos? Photon rate [10 3 counts s 1 ] (Answer: yes, the one on the left) 40 35 30 25 20 15 10 GRB931008 Trigger 2571 0 20 40 60 80 100 Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6
The fireball model internal collisions power law E 2 broken power law { nπ + p γ + (1232) pπ 0 central emitter 1 plasma shells propagate at different speeds π + µ + ν µ ν µe + ν eν µ π 0 γγ n (escapes) pe ν e 2 two shells collide + more ν production modes (NeuCosmA, HUMMMER+ PRL 2012) For each GRB, 3 the shells merge and particles are emitted Mészáros, Reese, Goodman, Pachinsky, et al. energy in neutrinos energy in gamma rays Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 7
UHECR emission in a collision UHECRs escape as Protons that leak out (not producing ν s) Neutrons, which decay into protons outside the source; or τ n < 1 optically thin to n escape p τ n 1 optically thick to n escape p p's trapped in bulk by magnetic field p p p p p p's can leak from borders p n n p's trapped in bulk by magnetic field p's, n's trapped in bulk by pγ and nγ interactions n p p n p n p n n p's, n's can leak from borders P. BAERWALD, MB, W. WINTER, ApJ 768, 186 (2013) P. BAERWALD, MB, W. WINTER, Astropart. Phys. 62, 66 (2015) See also: H. HE et al., ApJ 752, 29 (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 8
Multiple individual collisions An evolving fireball: 1000 expanding shells Different individual speeds Random initial speeds (Γ) follow a distribution Many collision radii (R C ) Falling γ, p densities fraction of energy output 0.30 0.25 0.20 0.15 0.10 0.05 0.00 photosphere n escape direct escape neutrinos UHECRs Γrays circumburst medium 8 9 10 11 12 log 10 R C km S. KOBAYASHI, T. PIRAN, R. SARI, ApJ 490, 92 (1997) F. DAIGNE, R. MOCHKOVITCH, MNRAS 296, 275 (1998) MB, P. BAERWALD, K. MURASE, W. WINTER, Nat. Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 9
Synthetic light curves Each collision emits a particle pulse their superposition yields a synthetic light curve: Log 10 (F/GeV cm -2 s -1 ) -3-4 -5-6 GRB 1-7 Gamma rays Neutrinos (all flavors) -8 0 20 40 60 80 t obs [s] Gamma-ray, neutrino count [a.u] 2000 1500 1000 500 Gamma rays 0 60 50 Neutrinos 40 30 20 10 0 0 20 40 60 80 t obs [s] MB, P. BAERWALD, K. MURASE, W. WINTER Nature Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 10
Synthetic light curves Each collision emits a particle pulse their superposition yields a synthetic light curve: Log 10 (F/GeV cm -2 s -1 ) -3-4 -5-6 Energy in gamma-rays: E iso γ,tot = 10 53 erg GRB 1-7 Gamma rays Neutrinos (all flavors) -8 0 20 40 60 80 t obs [s] T 90 59 s 1000 initial shells 990 collisions Gamma-ray, neutrino count [a.u] 2000 1500 1000 500 Gamma rays 0 60 50 Neutrinos 40 30 20 10 0 0 20 40 60 80 t obs [s] MB, P. BAERWALD, K. MURASE, W. WINTER Nature Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 10
Quasi-diffuse neutrino flux Assuming 667 identical GRBs per year:, Γ =222 0 7 10 8 10 9 10 10-2 s -1 sr -1 E 2 J νμ / GeV cm 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 b subphotospheric extrapolation evolving fireball this work IC40+59 stacking GRB limit standard numerical prediction Γ 0 =500, Γ =369 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E / GeV -2 s -1 sr -1 10-8 10-9 10-10 10 11 GeV cm10 2-11 s 1 sr 1 E 2 J νμ / GeV cm 10-12 10-13 10-14 dominant ten collisions 10-15 c 10-16 10 0 10 1 MB, P. BAERWALD, K. MURASE, W. WINTER Nature Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 11
Which GRB is brighter in neutrinos? Back to our initial question: Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 5 GRB920513 Trigger 1606 0 20 40 60 80 100 Time since trigger [s] Fast time variability can we tell which GRB is likely bright in neutrinos? Photon rate [10 3 counts s 1 ] 40 35 30 25 20 15 10 GRB931008 Trigger 2571 0 20 40 60 80 100 Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 12
What makes a GRB bright in neutrinos? Undisciplined GRB engine Broad Γ distribution E.g., engine emits shells with log-normal Γ distrib. Disciplined GRB engine Narrow Γ distribution E.g., engine emits shells with oscillating Γ MB, MURASE, WINTER, 1606.02325 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 13
Light curves Undisciplined GRB engine Fast variability dominates No broad pulses Disciplined GRB engine Broad pulses dominate Fast variability on top 80 Gamma-ray, Log neutrino count [a.u] 10 (F/GeV cm -2 s -1 ) 2000-3 140 GRB 5 Gamma rays 120 1500 100 1000-4 80 60 500 40-5 20 0 0 60 4-650 Neutrinos 3 40-7 30 2 20 1 10-8 0 0 0 20 40 60 80 80 t obs [s] MB, MURASE, WINTER, 1606.02325 Gamma-ray, neutrino count [a.u] Gamma rays Neutrinos 0 0 20 40 60 80 t obs [s] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 14
How many optically thick collisions? Undisciplined GRB engine Shells have very different speeds Collide quickly, close to center High p and γ densities 10 collisions near photosphere are optically thick 10 6 10 7 10 8 10 9 10 10 10 11 10 12-10 -5 0 5 R C /km log 10 (τpγ) Disciplined GRB engine Shells have similar speeds Collide far from center Low p and γ densities All (superphotospheric) collisions are optically thin 10 6 10 7 10 8 10 9 10 10 10 11 10 12-10 -5 0 R C /km log 10 (τpγ) below photosphere opt. thick opt. thin MB, MURASE, WINTER, 1606.02325 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 15
So which burst is neutrino-bright? Undisciplined GRB engine 10 11 10 2 GeV 10 3 10cm 4 1 5 10s 6 1 10 7 sr 10 1 8 10 9 10 10 5 10 13 2 10 3 GeV 10 4 10cm 5 1 6 10s 7 1 10 8 sr 10 1 9 10 10 E [GeV] E [GeV] 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] E 2 J νμ [GeV 10-12 10-13 10-14 10-15 10 10-8 -8 10 10-9 -9 10 10-10 -10 subphotospheric extrap. multi-zone one-zone 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 10-8 10-9 IC 2016 GRB limit 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10 10-8 -8 10 10-9 -9 10 10-10 -10 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 MB, MURASE, WINTER, 1606.02325 GRB 4 1 sr -1 ] 10-12 10-13 10-14 Disciplined GRB engine 10-15 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB2 5 Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves -10 16 E 2 J νμ [GeV 10-8 10-9 GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] 2 2-2 -1-1
So which burst is neutrino-bright? Undisciplined GRB engine 10 11 10 2 GeV 10 3 10cm 4 1 5 10s 6 1 10 7 sr 10 1 8 10 9 10 10 5 10 13 2 10 3 GeV 10 4 10cm 5 1 6 10s 7 1 10 8 sr 10 1 9 10 10 E [GeV] E [GeV] 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] E 2 J νμ [GeV 10-12 10-13 10-14 10-15 10 10-8 -8 10 10-9 -9 10 10-10 -10 subphotospheric extrap. multi-zone Good ν emitter one-zone 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 10-8 10-9 IC 2016 GRB limit 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10 10-8 -8 10 10-9 -9 10 10-10 -10 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 MB, MURASE, WINTER, 1606.02325 GRB 4 1 sr -1 ] 10-12 10-13 10-14 Disciplined GRB engine 10-15 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB2 5 Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves -10 16 E 2 J νμ [GeV 10-8 10-9 Poor ν emitter GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] 2 2-2 -1-1
So which burst is neutrino-bright? Undisciplined GRB engine 10 11 10 2 GeV 10 3 10cm 4 1 5 10s 6 1 10 7 sr 10 1 8 10 9 10 10 5 10 13 2 10 3 GeV 10 4 10cm 5 1 6 10s 7 1 10 8 sr 10 1 9 10 10 E [GeV] E [GeV] 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] E 2 J νμ [GeV 10-12 10-13 10-14 10-15 10 10-8 -8 10 10-9 -9 10 10-10 -10 subphotospheric extrap. multi-zone Good ν emitter one-zone 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 10-8 10-9 IC 2016 GRB limit 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10 10-8 -8 10 10-9 -9 10 10-10 -10 10 10-11 -11 10 10-12 -12 10 10-13 -13 10 10-14 -14 10 10-15 -15 10 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 10 8 10 8 10 9 10 9 10 10 E E [GeV] GRB2 5 MB, MURASE, WINTER, 1606.02325 An undisciplined engine makes a GRB neutrino-bright GRB 4 GRB 5 1 sr -1 ] 10-12 10-13 10-14 Disciplined GRB engine 10-15 Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves -10 16 E 2 J νμ [GeV 10-8 10-9 Poor ν emitter E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ] 2 2-2 -1-1
Using our new insight Log 10 (F/GeV cm -2 s -1 ) Log 10 (F/GeV cm -2 s -1 ) -3-4 -5-6 GRB 1-7 Gamma rays Neutrinos (all flavors) -8 0 20 40 60 80 t obs [s] -3-4 -5-6 -7 GRB 4-8 0 20 40 60 80 t obs [s] 2000-3 GRB 2 1500 1000-4 Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma rays 500-5 0 60-6 50 Neutrinos 40-7 30 20 10-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] 700-3 600 500 GRB 5 Gamma rays 400-4 300 200 100-5 0 700 600-6 Neutrinos 500 400 300-7 200 100-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] MB, MURASE, WINTER, 1606.02325 Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) 800-3 GRB Gamma 3 rays 600 400-4 200-5 0 600 500-6 Neutrinos 400 300-7 200 100-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] 140-3 120 100-4 80 60 40-5 20 0 4-6 3-7 2 1 GRB 6 Gamma rays Neutrinos -8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] Gamma-ray, neutrino count [a.u] Gamma-ray, neutrino count [a.u] 50 40 30 20 10 0 1.0 0.8 0.6 0.4 0.2 0.0 800 600 400 200 0 140 120 100 80 60 40 20 0 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17
Using our new insight Log 10 (F/GeV cm -2 s -1 ) Log 10 (F/GeV cm -2 s -1 ) -3-4 -5-6 GRB 1-7 Gamma rays Neutrinos (all flavors) -8 0 20 40 60 80 t obs [s] -3-4 -5-6 -7 GRB 4-8 0 20 40 60 80 t obs [s] 2000-3 GRB 2 1500 1000-4 Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma rays 500-5 0 60-6 50 Neutrinos 40-7 30 20 10-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] 700-3 600 500 GRB 5 Gamma rays 400-4 300 200 100-5 0 700 600-6 Neutrinos 500 400 300-7 200 100-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] MB, MURASE, WINTER, 1606.02325 Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) Gamma-ray, neutrino count [a.u] Log 10 (F/GeV cm -2 s -1 ) 800-3 GRB Gamma 3 rays 600 400-4 200-5 0 600 500-6 Neutrinos 400 300-7 200 100-8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] Good ν emitter Good ν emitter Poor ν emitter 140-3 120 100-4 80 60 40-5 20 0 4-6 3-7 2 1 GRB 6 Gamma rays Good ν emitter Poor ν emitter Poor ν emitter Neutrinos -8 0 0 20 40 40 60 60 80 80 t obs t obs [s] [s] Gamma-ray, neutrino count [a.u] Gamma-ray, neutrino count [a.u] 50 40 30 20 10 0 1.0 0.8 0.6 0.4 0.2 0.0 800 600 400 200 0 140 120 100 80 60 40 20 0 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17
Using our new insight E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 subphotospheric extrap. multi-zone one-zone 10-11 10-12 10-13 10-14 IC 2016 GRB limit 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 1 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] GRB 4 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 2 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] MB, MURASE, WINTER, 1606.02325 GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 3 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] GRB 6 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17
Using our new insight E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 subphotospheric extrap. multi-zone one-zone 10-11 10-12 10-13 10-14 IC 2016 GRB limit 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 1 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] GRB 4 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 2 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] MB, MURASE, WINTER, 1606.02325 GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] GRB 3 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] GRB 6 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17
Using our new insight E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-8 10-8 10-8 IC 2016 10-9 GRB limit GRB 1 10-9 GRB 2 10-9 GRB 3 10-10 subphotospheric extrap. multi-zone Good ν emitter one-zone 10-10 Good ν emitter 10-10 Poor ν emitter 10-11 10-11 10-11 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E [GeV] 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-12 10-13 10-14 E [GeV] 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] 10-8 10-8 GRB 4 10-9 GRB 5 10-9 GRB 6 Good ν emitter 10-10 Poor ν emitter 10-10 Poor ν emitter 10-11 10-11 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] MB, MURASE, WINTER, 1606.02325 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 10-12 10-13 10-14 10-15 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E [GeV] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17
Time delays in gamma-ray light curves Neutrino-weak bursts show time delays in different energy bands Photon count [a.u.] 120 10 6 10 2 GeV 80 Fermi-GBM GRB 5 40 0 120 80 40 0 10 1 10 2 GeV Fermi-LAT 120 80 10 2 10 6 GeV CTA 40 0 0 20 40 60 80 t obs [s] MB, MURASE, WINTER, 1606.02325 See also: BOŠNJAK, DAIGNE, A&A 568, A45 (2014) [1404.4577] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 18
Time delays in gamma-ray light curves Neutrino-weak bursts show time delays in different energy bands Photon count [a.u.] 120 10 6 10 2 GeV 80 Fermi-GBM GRB 5 40 0 120 80 40 0 10 1 10 2 GeV Fermi-LAT 120 80 10 2 10 6 GeV CTA 40 0 0 20 40 60 80 t obs [s] MB, MURASE, WINTER, 1606.02325 See also: BOŠNJAK, DAIGNE, A&A 568, A45 (2014) [1404.4577] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 18
The future GRBs could be the first resolved high-energy neutrino sources We have a new criterion to select promising GRBs We will add more emission models to our technique We need next-gen neutrino telescopes (IceCube-Gen2, KM3NeT) Next step: ready our technique for application to data Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 19
Backup slides Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 20
What are the ingredients? To calculate the ν flux from a GRB, we need: Its gamma-ray luminosity L iso γ [erg s 1 ] [measured] Its variability timescale t v [s], from the light curve [measured] Break energy of its photon spectrum ɛ γ,break [MeV] [measured] Its redshift z [(sometimes) measured] The bulk Lorentz factor of its jet Γ [estimated] The energy in electrons, magnetic field, protons [estimated] Now let us cook up the neutrinos Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 21
Normalizing neutrinos with observed gamma rays For each GRB, energy in neutrinos energy in gamma rays 0 de ν E ν F ν (E ν ) = 1 8 [1 (1 x p π ) R/λpγ ] }{{} f π: fraction of total p energy given to π s 1 f e 10 MeV 1 kev R: size of the emitting region λ pγ : mean free path for pγ interactions x p π : avg. fraction of p energy transferred to a π in one interaction f 1 e dɛ γ ɛ γ F γ (ɛ γ ) : ratio of energy in protons to energy in photons ( baryonic loading ) ( ) (0.01 Optical depth to pγ : R L iso ) ( ) γ 10 2.5 4 ( MeV = λ pγ 10 52 erg s 1 Γ t v ε γ,break ) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 22
Cooking up the neutrinos Observed gamma-ray fluence [GeV 1 cm 2 ] F γ ( εγ ) { ( εγ /ε γ,br ) 1, ε γ < ε γ,br = 1 MeV ( εγ /ε γ,br ) 2.2, ε γ ε γ,br + Assumed proton spectrum in the source N ( ) 2 p Ep E p = 10?2 NeuCosmA 2011 E ν,br : from photon spectrum E ν,µ: from µ synchrotron IC?FC cooling E Ν 2 FΝ?EΝ??GeV cm?2? 10?3 10?4 Neutrinos from pγ, via resonance ( Eν ) αν, E ν < E ν,br E ( ν,br ) βν Eν F ν (E ν ), E ν,br E ν < E ν,µ E ( ν,br ) βν ( ) 2 Eν Eν, E ν E ν,µ E ν,br E ν,µ 10?5 10 4 10 5 10 6 10 7 10 8 10 9 EΝ?GeV? E. WAXMAN, J. N. BAHCALL, PRL 78, 2292 (1997) D. GUETTA et al., Astropart. Phys. 20, 429 (2004) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 23
Refining the neutrino spectrum NeuCosmA More production channels, more complete particle-physics treatment For example, GRB080603A: 1. Correction to analytical model (IC-FC RFC) 2. Change due to full numerical calculation IC-FC: RFC: NFC: IceCube-Fireball Calculation Revised Fireball Calculation Numerical Fireball Calculation S. HÜMMER, P. BAERWALD, W. WINTER, PRL 108, 231101 (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 24
Neutrino spectra (at Earth) 10 7 Electron neutrino spectrum NeuCosmA 2010 10 7 Muon neutrino spectrum NeuCosmA 2010 E 2 Φ ΝeΝe GeV sr 1 s 1 cm 2 10 8 10 9 Total flux Ν Μ WB flux Ν e E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 Total flux rescaled Total flux Ν e Ν Μ WB flux 10 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 EGeV Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 25
Diffuse fluxes at Earth E 3 J CR GeV 2 cm 2 s 1 sr 1 10 4 10 3 10 2 10 1 Α p 2.0 Neutron model vs. two-component model: prompt and cosmogenic ν s UHECRs CR neutron dominated #1 Χ 2 d.o.f. 3.31 f e 1 41 CR leakage dominated #2 f 1 e 62 Χ 2 d.o.f. 5.95 10 9 10 10 10 11 10 12 10 13 10 14 Neutrinos NeuCosmA 2014 10 0 10 7 10 8 10 9 10 10 10 11 10 15 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 P. BAERWALD, MB, W. WINTER, ApJ 768, 186 (2013) P. BAERWALD, MB, W. WINTER, Astropart. Phys. 62, 66 (2015) See also: H. HE et al., ApJ 752, 29 (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 26
A simplifying assumption: identical collisions All internal collisions are identical and occur at the same radius C 2 v l' = Γct (1+z) ~ 9 10 (1+z) km R = 2cΓ t /(1+z) ~ 5 10 /(1+z) km v Γ = 300-3 typical values: t v = 10 s T 90 = 10 s N coll T 90 /t v 100 1000 identical collisions Calculate particle emission spectra once Then multiply by N coll Γ is the average speed of shells 7 4 r Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 27
Initial distribution of shell speeds Distribution of initial shell speeds (Lorentz factors): ( ) Γk,0 1 ln = A Γ x Γ 0 1 x follows a Gaussian distribution, P (x) dx = dx e x 2 /2 / 2π 0.012 0.010 0 300 A 0.1 A Γ < 1 Speeds too similar, collisions only at large radii pdfk,0 0.008 0.006 A 2.0 0.004 A 1.0 0.002 0.000 0 100 200 300 400 0 k,0 A Γ 1 Spread too large, too many collisions at low radii A Γ 1 Just right, burst has high efficiency of conversion of kinetic to radiated energy Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 28
Anatomy of an internal collision 1 Propagation 2 Collision 3 Radiation fast shell Γ f slow shell Γ s reverse shock forward shock m f m s m m m + m f merged shell s γ Γ m ν p Γ f Γ s l f ls l < l, l m f s n Part of the initial kinetic energy radiated as γ s, ν s, p s, and n s: ( ) ( ) Ecoll iso = Ekin,f iso E kin,m iso + Ekin,m iso E kin,s iso 1/12 1/12 5/6 ɛ ee iso coll }{{} ɛ B E iso coll }{{} ɛ pe iso coll }{{} energy in photons energy in magnetic fields energy in baryons Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 29
Tracking each collision individually Each collision occurs in a different emission regime 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 R Ckm E 2 ΝΜ GeVcm2 neutrinos subphotospheric opt. thick to n's direct p escape 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 R Ckm Ep,maxGeV cosmic rays UHECR 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 4 10 3 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 R Ckm EΓ,maxGeV gammarays GBM LAT CTA ν µ + ν µ fluence maximum p energy maximum γ energy (observer s frame) (source frame) MB, P. BAERWALD, K. MURASE, W. WINTER, Nat. Commun. 6, 6783 (2015) Sub-photospheric: τ eγ > 1 Limited by γ + γ e + + e Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 30
NeuCosmA: (revised) GRB particle emission I Two ingredients: ( E p ) N p NeuCosmA }{{} proton density at the source [GeV 1 cm 3 ] N γ = Q ν ( ) E }{{ ν } emitted neutrino spectrum [GeV 1 cm 3 s 1 ] Photons (same shape as observed at Earth): N γ ( E γ ) = ( E γ ) }{{} photon density at the source ( E γ /E γ,break ) 1, E γ,min = 0.2 ev E γ < E γ,break = 1 kev ( E γ /E γ,break ) 2.2, E γ E γ,break 0, otherwise Protons: N p ( E p ) E α p p e E p /E p,max (α p 2) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 31
NeuCosmA: (revised) GRB particle emission I Two ingredients: ( E p ) N p NeuCosmA }{{} proton density at the source [GeV 1 cm 3 ] N γ = Q ν ( ) E }{{ ν } emitted neutrino spectrum [GeV 1 cm 3 s 1 ] Photons (same shape as observed at Earth): N γ ( E γ ) = Protons: N p ( E γ ) }{{} photon density at the source ( E γ /E γ,break ) 1, E γ,min = 0.2 ev E γ < E γ,break = 1 kev ( E γ /E γ,break ) 2.2, E γ E γ,break 0, otherwise t acc ( E p ) E α p p e E p /E p,max (α p 2) ( E ) [ p,max = min t ( dyn, t syn E ) p,max, t ( pγ E )] p,max Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 31
NeuCosmA: (revised) GRB particle emission II Normalize the particle densities at the source Photons: photon energy density per collision = }{{} E γ N γ(e γ) de γ E iso, γ,tot 1053 erg (from observed fluence) {}}{ total gamma-ray energy of burst number of collisions }{{} N coll volume of one collision }{{} V iso Protons: baryonic loading (energy in p s / energy in e s + γ s), e.g., 10 proton energy density per collision = 1 photon energy density per collision }{{} f e E p N p(e p) de p Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 32
NeuCosmA: (revised) GRB particle emission III Injected/ejected spectrum of secondaries (π, K, n, ν, etc.): Q ( E ) = de p E E p N p ( ) E p c de γ N γ ( ) ( ) E γ R x, y R contains cross sections, multiplicities for different channels 0 x E /E p y E pe γ/ (m pc 2) response function What does NeuCosmA include? 10 7 NeuCosmA 2010 Total flux pγ + (1232) π 0, π +,... extra K, n, π, multi-π prod. modes synchrotron losses of secondaries adiabatic cooling full photon spectrum E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 tchannel Multi Π WB approx. Higher resonances WB flux 1232 only neutrino flavor transitions 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 33
NeuCosmA the full photohadronic cross section 10 7 NeuCosmA 2010 E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 WB approx. WB flux 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34
NeuCosmA the full photohadronic cross section Contributions to (ν µ + ν µ) flux from π ± decay divided in: (1232)-resonance 10 7 NeuCosmA 2010 E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 WB approx. WB flux 1232 only P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34
NeuCosmA the full photohadronic cross section Contributions to (ν µ + ν µ) flux from π ± decay divided in: (1232)-resonance 10 7 NeuCosmA 2010 Higher resonances E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 WB approx. WB flux Higher resonances 1232 only P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34
NeuCosmA the full photohadronic cross section Contributions to (ν µ + ν µ) flux from π ± decay divided in: (1232)-resonance 10 7 NeuCosmA 2010 Higher resonances t-channel (direct production) P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 tchannel WB approx. Higher resonances WB flux 1232 only 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34
NeuCosmA the full photohadronic cross section Contributions to (ν µ + ν µ) flux from π ± decay divided in: (1232)-resonance 10 7 NeuCosmA 2010 Total flux Higher resonances t-channel (direct production) High energy processes (multiple π) P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm 2 10 8 10 9 tchannel Multi Π WB approx. Higher resonances WB flux 1232 only 10 10 10 3 10 4 10 5 10 6 10 7 10 8 Especially "Multi π" contribution leads to change of flux shape; neutrino flux higher by up to a factor of 3 compared to WB treatment Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34
NeuCosmA further particle decays π + µ + + ν µ µ + e + + ν e + ν µ π µ + ν µ µ e + ν e + ν µ K + µ + + ν µ n p + e + ν e Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 35
NeuCosmA further particle decays Resulting ν e flux (at the observer) π + µ + + ν µ µ + e + + ν e + ν µ 10 7 NeuCosmA 2010 Total flux π µ + ν µ µ e + ν e + ν µ K + µ + + ν µ n p + e + ν e E 2 Φ Νe Νe GeV sr1 s 1 cm 2 10 8 10 9 10 10 from Μ WB flux from n 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 35
NeuCosmA further particle decays Resulting ν µ flux (at the observer) π + µ + + ν µ 10 7 NeuCosmA 2010 µ + e + + ν e + ν µ Total flux from Μ π µ + ν µ, µ e + ν e + ν µ K + µ + + ν µ E 2 Φ ΝΜ ΝΜ GeV sr1 s 1 cm 2 10 8 10 9 WB flux from Π n p + e + ν e 10 10 from K 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, 067303 (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 35
NeuCosmA how the neutrino spectrum changes I E Ν 2 F ΝEΝ GeV cm 2 10 2 NeuCosmA 2011 10 3 10 4 10 5 ICFC RFC c fπ c s shape revised 10 4 10 5 10 6 10 7 10 8 S. HÜMMER, P. BAERWALD, W. WINTER, Phys. Rev. Lett. 108, 231101 (2012) f CΓ f f Σ Corrections to the analytical model: shape revised: shift of first break (correction of photohadronic threshold) different cooling breaks for µ s and π s (1 + z) correction on the variability scale of the GRB Correction cf π to π prod. efficiency: f Cγ : full spectral shape of photons f = 0.69: rounding error in analytical calculation f σ 2/3: from neglecting the width of the -resonance Correction c S : energy losses of secondaries energy dependence of the mean free path of protons Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 36
Neutron model of UHECR emission under tension? In 2012, IceCube ruled this analytical version of the fireball model assumed a fixed baryonic loading of 10 extrapolated diffuse ν flux from 117 215 GRBs ( quasi-diffuse ) analytical calculation in tension with upper bounds ICECUBE, Nature 484, 351 (2012) M. AHLERS et al. Astropart. Phys. 35, 87 (2011) D. GUETTA et al. Astropart. Phys. 20, 429 (2004) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 37
The new prediction of the quasi-diffuse GRB ν flux Repeat the IceCube GRB neutrino analysis, with NeuCosmA Same GRB sample and parameters Calculate ν fluence for each burst and stacked fluence F ν (E ν) Quasi-diffuse flux (N GRB = 117): φ ν (E ν) = F ν (E 1 1 667 bursts ν) 4π N GRB yr E Ν 2 Φ ΝE GeV cm 2 s 1 sr 1 10 9 10 10 NeuCosmA 2012 IC40 IC4059 NFC prediction GRB, all GRB, z known stat. error astrophysical uncertainties 1 100 50 20 f e 10 5 Flux 1 order of magnitude lower! IC86, 10y extrapolated 10 5 10 6 10 7 10 8 S. HÜMMER, P. BAERWALD, W. WINTER, PRL 108, 231101 (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 38
Improved IceCube bounds (2014) Only upgoing ν µ s with > 1 TeV used Four years of data (IC-40, -59, -79, -86) Larger GRB catalogue (506 bursts) One coincident event found, with low statistical significance 1% of the diffuse flux can be from prompt GRB emission ε 2 b Φ0 (GeV cm 2 s 1 sr 1 ) 10 7 10 8 10 9 10 10 Ahlers et al. Waxman-Bahcall 90% 68% 50% 10 4 10 5 10 6 10 7 Neutrino break energy εb (GeV) 100 90 80 70 60 50 Exclusion CL (%) fp 100 30 10 3 Standard 90% 50% 68% 100 200 300 400 500 600 700 800 900 Γ 100 90 80 70 60 50 Exclusion CL (%) [ICECUBE, ApJ 805, L5 (2015)] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 39
A two-component model of CR emission Optical depth: τ n = t 1 pγ t 1 dyn = Ep,max { 1, optically thin source > 1, optically thick source Particles can escape from within a shell of thickness λ mfp : λ ( p,mfp E ) = min [ r, R L ( E ), ct pγ ( E )] } λ ( n,mfp E ) = min [ r, ct pγ ( E )] f esc = λ mfp r fraction of escaping particles Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 40
We need direct proton escape Scan of the GRB emission parameter space acceleration efficiency η = 0.1 η = 1.0 LAT visible 1000 800 Η 0.1 4 Η 1.0 3 NeuCosmA 2013 10 1 1000 Η 0.1Η 1.0 10 53 600 400 1 z direct escape 2 200 direct escape 0 10 50 10 50 10 51 10 51 10 52 10 52 optically thick LAT invisible 800 no n escape at high efficiencies! NeuCosmA 2013 10 1 neutron escape optically thin to n escape optically thick to n escape LAT L Γ,iso ergs invisible 1 tvs 10 2 600 400 full Σ pγ 200 10 3 10 50 10 50 10 51 10 51 10 52 10 52 10 53 L Γ,iso ergs 1 P. BAERWALD, MB, AND W. WINTER, ApJ 768, 186 (2013) WB resonance we need high efficiencies direct proton escape is required tvs 10 2 10 3 10 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 41
A two-component model of UHECR emission Sample neutrino fluences Optically thin source Optically thick source P. BAERWALD, MB, W. WINTER, ApJ 768, 186 (2013) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 42
Cosmogenic neutrinos We have seen that protons interact with the cosmological photon fields (CMB, etc.), e.g., p + γ + π + + n, and neutrinos are created in the decays of the secondaries: π + µ + + ν µ µ + ν µ + ν e + e + n p + e + ν e These are called cosmogenic neutrinos Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 43
Cosmogenic neutrinos 10 6 E 2 JΝ all flavours GeV cm 2 s 1 sr 1 10 7 10 8 10 9 10 10 10 11 IC 201212 diffuse UHE allflavor limit total interactions with CMB interactions with CIB NeuCosmA 2014 neutron decay 10 12 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 2 P. BAERWALD, MB, W. WINTER, Astropart. Phys. 62, 66 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 43
ν s in the GRB internal shock model Secondary injection of neutrons, neutrinos (GeV 1 cm 3 s 1 ) Q (E ) = de p E E p N p ( ) E p cdε N γ (ε ) R ( E, E p, ε ) 0 Normalisation to the observed GRB photon flux F γ ε N γ (ε ) dε = E iso sh V iso F γ, E pn p ( ) E p de p = 1 E iso sh f e V iso F γ f e Fluence per shell, at Earth (GeV 1 cm 2 ) F sh = t v V iso (1 + z) 2 4πdL 2 Q Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 44
ν s in the GRB internal shock model Secondary injection of neutrons, neutrinos (GeV 1 cm 3 s 1 ) Q (E ) = de p E E p N p ( ) E p cdε N γ (ε ) R ( E, E p, ε ) 0 Photon density, shock rest frame (GeV 1 cm 3 ): { N γ (ε (ε ) αγ, ε γ,min ) = 0.2 ev ε ε γ,break (ε ) βγ, ε γ,break ε ε γ,max = 300 ε γ,min ε γ,break = O (kev), α γ 1, β γ 2 Proton density: N p ( ) ( ) [ E p E αp p exp ( E p/e p,max ) ] 2 (α p 2) Maximum proton energy limited by energy losses: t acc ( ) [ E p,max = min t dyn, t syn ( ) ( )] E p,max, t pγ E p,max Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 44
ν s in the GRB internal shock model Secondary injection of neutrons, neutrinos (GeV 1 cm 3 s 1 ) Q (E ) = de p E E p N p ( ) E p cdε N γ (ε ) R ( E, E p, ε ) 0 Normalisation to the observed GRB photon flux F γ ε N γ (ε ) dε = E iso sh V iso F γ, E pn p ( ) E p de p = 1 E iso sh f e V iso F γ f e Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 44
ν s in the GRB internal shock model Secondary injection of neutrons, neutrinos (GeV 1 cm 3 s 1 ) Q (E ) = de p E E p N p ( ) E p cdε N γ (ε ) R ( E, E p, ε ) 0 Normalisation to the observed GRB photon flux F γ ε N γ (ε ) dε = E iso sh V iso F γ, E pn p ( ) E p de p = 1 E iso sh f e V iso F γ f e Fluence per shell, at Earth (GeV 1 cm 2 ) F sh = t v V iso (1 + z) 2 4πdL 2 Q Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 44
Gamma-ray and neutrino pulses A fast-rise-exponential-decay (FRED) gamma-ray pulse is emitted in every collision: 55 LΓ L Γ peak t rise l m, m, s, f, z t obs log 10 L Γ peak erg s 1 50 45 40 7 8 9 10 11 12 log 10 R C km L peak γ R 2 C Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 45
The prediction is robust -2 s -1 sr -1 Simulations show only weak dependence of the flux on the boost Γ... E 2 J νμ / GeV cm -2 s -1 sr -1 10-8 10-9 10-10 10-11 10-12 10-13 10-14 a 10-15 Γ 0=300, Γ =222 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm 10-8 10-9 10-10 10-11 10-12 10-13 10-14 b subphotospheric extrapolation evolving fireball IC40+59 stacking GRB limit standard numerical prediction 10-15 Γ 0=500, Γ =369 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E / GeV... and on the GRB engine variability time δt eng E 2 J νμ / GeV cm 10-8 10-9 10-10 10-11 10-12 10-13 10-14 a subphotospheric extrapolation evolving fireball IC40+59 stacking GRB limit standard numerical prediction 10-15 N sh=1000, N coll=794 δt eng =0.1s, t v=0.67s 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm 10-8 10-9 10-10 10-11 10-12 10-13 10-14 b 10-15 N sh=1000, N coll=457 δt eng =1.0s, t v=11.89s 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm -2 s -1 sr -1 E 2 J νμ / GeV cm 10-8 10-9 10-10 10-11 10-12 10-13 10-14 c 10-15 Γ 0=1000, Γ =779 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10-8 10-9 10-10 10-11 10-12 10-13 10-14 E / GeV 10-15 N sh=100, N coll=87-97 δt eng =0.1s, t v=0.53-0.66s 10-16 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 46 c E / GeV
Accelerating iron Photodisintegration destroys nuclei close to the center ( 10 8 km) e.g., ANCHORDOQUI et al., Astropart. Phys. 29, 1 (2008) However, they can survive at large radii: 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 R C / km E Fe,max / GeV UHECR iron photodis.-limited adiabatic-limited Γ 0 =500, Γ =369 MB, BAERWALD, MURASE, WINTER Nature Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 47
Contribution of GRBs to the diffuse ν flux Three populations: high-luminosity long GRBs (HL-GRB), low-luminosity long GRBs (LL-GRB), short GRBs (sgrb) Sub-PeV: GRBs contribute a few % to the IceCube diffuse flux PeV: contribution could be higher I. TAMBORRA, S. ANDO, JCAP 1509, 036 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 48
Initialising the burst simulation Initial number of plasma shells in the jet: 1000 Γ Γ Γ Γ Γ N,0 1,0 2,0 3,0 4,0... sh d d d d t = 0 l l l l l Initial values of shell parameters: Width of shells and separation between them: l = d = c δt eng Equal kinetic energy for all shells ( 10 52 erg) Shell speeds Γ k,0 follow a distribution (log-normal or other) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 49
Propagating and colliding the shells Γ Γ Γ Γ Γ N,0 1,0 2,0 3,0 4,0... sh d d d d l l l l l Γ Γ Γ Γ Γ N sh,0 1,0 2,0 3,0 4,0... t = 0 During propagation: speeds, masses, widths do not change (only in collisions) the new, merged shells continue propagating and can collide again l l l l l Γ Γ Γ 2,0 Γ Γ 4,0... N sh,0 3,0 1,0 l l l l l l Γ Γ Γ m 4,0... Γ N sh,0 1,0 lm l l R C t Evolution stops when either: a single shell is left; or all remaining shells have reached the circumburst medium ( 6 10 11 km) final number of collisions number of initial shells ( 1000) S. KOBAYASHI, T. PIRAN, R. SARI, ApJ 490, 92 (1997) F. DAIGNE, R. MOCHKOVITCH, MNRAS 296, 275 (1998) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 50
How is the new prediction different? The top-contributing collisions are at the photosphere Pion production efficiency there is independent of Γ: f ph pγ 5 ε 0.25 ɛ e 0.1 1 kev ɛ γ,break ε: energy dissipation efficiency ɛ e : fraction of dissipated energy as e.m. output (photons) Time-integrated neutrino fluence dominated is independent of Γ: F ν N coll (f pγ 1) N tot coll [ min 1, fpγ ph ] ɛ p ɛ e E iso γ tot Compare to standard predictions, which have a Γ 4 dependence Raising ɛ p automatically decreases ɛ e, so the photosphere grows, but still 10 photospheric collisions dominate Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 51
How is the new prediction different? The top-contributing collisions are at the photosphere Pion production efficiency there is independent of Γ: f ph pγ 5 ε 0.25 ɛ e 0.1 1 kev ɛ γ,break ε: energy dissipation efficiency ɛ e : fraction of dissipated energy as e.m. output (photons) Time-integrated neutrino fluence dominated is independent of Γ: F ν N 10 10 coll (f pγ 1) [ ] 10 53 Ncoll tot min 1, fpγ ph ɛ erg p Eγ tot iso ɛ e 1000 Compare to standard predictions, which have a Γ 4 dependence Raising ɛ p automatically decreases ɛ e, so the photosphere grows, but still 10 photospheric collisions dominate Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 51
What about low-luminosity and choked GRBs? Low-luminosity and choked GRBs might be in the same family as high-luminosity long GRBs Due to lower jet speeds (Γ b ), they do not break out They might explain the TeV region of the IceCube diffuse ν flux:!" ' 4! #,/! 94! :,5617,0; #,<!,<=! 8!" (!" )!" *!"!" +,-,$ $,-,,-,!" +!",-, +,-,!$" /0123+1 +,.,!$"!"!!!" #!" $!" %!" &!" '!" (!" )!" *!"!" 4!,56178 I. TAMBORRA, S. ANDO, PRD 93, 053010 (2016) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 52