Multi-messenger light curves from gamma-ray bursts

Transcription

1 Multi-messenger light curves from gamma-ray bursts , 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

2 Why are GRBs natural ν source candidates? 1 They are bright erg in gamma rays (Sun: erg in 1 yr; SN: 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

3 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

4 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

5 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

6 Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] GRB Trigger 1606 Photon rate [10 3 counts s 1 ] GRB Trigger Time since trigger [s] Time since trigger [s] can we tell which GRB is likely bright in neutrinos? Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6

7 Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] GRB Trigger Time since trigger [s] Fast time variability can we tell which GRB is likely bright in neutrinos? Photon rate [10 3 counts s 1 ] GRB Trigger Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6

8 Which GRB is brighter in neutrinos? Just from looking at these gamma-ray light curves, Photon rate [10 3 counts s 1 ] GRB Trigger 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) GRB Trigger Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 6

9 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

10 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

11 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 photosphere n escape direct escape neutrinos UHECRs Γrays circumburst medium 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

12 Synthetic light curves Each collision emits a particle pulse their superposition yields a synthetic light curve: Log 10 (F/GeV cm -2 s -1 ) GRB 1-7 Gamma rays Neutrinos (all flavors) t obs [s] Gamma-ray, neutrino count [a.u] Gamma rays Neutrinos 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

13 Synthetic light curves Each collision emits a particle pulse their superposition yields a synthetic light curve: Log 10 (F/GeV cm -2 s -1 ) Energy in gamma-rays: E iso γ,tot = erg GRB 1-7 Gamma rays Neutrinos (all flavors) t obs [s] T s 1000 initial shells 990 collisions Gamma-ray, neutrino count [a.u] Gamma rays Neutrinos 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

14 Quasi-diffuse neutrino flux Assuming 667 identical GRBs per year:, Γ = s -1 sr -1 E 2 J νμ / GeV cm b subphotospheric extrapolation evolving fireball this work IC40+59 stacking GRB limit standard numerical prediction Γ 0 =500, Γ = E / GeV -2 s -1 sr GeV cm s 1 sr 1 E 2 J νμ / GeV cm dominant ten collisions c MB, P. BAERWALD, K. MURASE, W. WINTER Nature Commun. 6, 6783 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 11

15 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 ] GRB Trigger Time since trigger [s] Fast time variability can we tell which GRB is likely bright in neutrinos? Photon rate [10 3 counts s 1 ] GRB Trigger Time since trigger [s] Slow pulse + fast variability Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 12

16 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, Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 13

17 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 ) GRB 5 Gamma rays Neutrinos t obs [s] MB, MURASE, WINTER, Gamma-ray, neutrino count [a.u] Gamma rays Neutrinos t obs [s] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 14

18 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 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 R C /km log 10 (τpγ) below photosphere opt. thick opt. thin MB, MURASE, WINTER, Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 15

19 So which burst is neutrino-bright? Undisciplined GRB engine GeV cm s sr GeV cm s sr 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 subphotospheric extrap. multi-zone one-zone IC 2016 GRB limit E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] MB, MURASE, WINTER, GRB 4 1 sr -1 ] Disciplined GRB engine E E [GeV] GRB2 5 Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves E 2 J νμ [GeV GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ]

20 So which burst is neutrino-bright? Undisciplined GRB engine GeV cm s sr GeV cm s sr 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 subphotospheric extrap. multi-zone Good ν emitter one-zone IC 2016 GRB limit E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] MB, MURASE, WINTER, GRB 4 1 sr -1 ] Disciplined GRB engine E E [GeV] GRB2 5 Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves E 2 J νμ [GeV Poor ν emitter GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ]

21 So which burst is neutrino-bright? Undisciplined GRB engine GeV cm s sr GeV cm s sr 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 subphotospheric extrap. multi-zone Good ν emitter one-zone IC 2016 GRB limit E E [GeV] GRB1 4 2 νμ [GeV cm -2-1 sr -1 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E E [GeV] GRB2 5 MB, MURASE, WINTER, An undisciplined engine makes a GRB neutrino-bright GRB 4 GRB 5 1 sr -1 ] Disciplined GRB engine Mauricio Bustamante -10 (CCAPP OSU) Multi-messenger GRB light curves E 2 J νμ [GeV Poor ν emitter E 2 J νμ [GeV cm -2 s -1 sr -1 ] 1 sr -1 ]

22 Using our new insight Log 10 (F/GeV cm -2 s -1 ) Log 10 (F/GeV cm -2 s -1 ) GRB 1-7 Gamma rays Neutrinos (all flavors) t obs [s] GRB t obs [s] GRB 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 Neutrinos t obs t obs [s] [s] GRB 5 Gamma rays Neutrinos t obs t obs [s] [s] MB, MURASE, WINTER, 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 ) GRB Gamma 3 rays Neutrinos t obs t obs [s] [s] GRB 6 Gamma rays Neutrinos t obs t obs [s] [s] Gamma-ray, neutrino count [a.u] Gamma-ray, neutrino count [a.u] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17

23 Using our new insight Log 10 (F/GeV cm -2 s -1 ) Log 10 (F/GeV cm -2 s -1 ) GRB 1-7 Gamma rays Neutrinos (all flavors) t obs [s] GRB t obs [s] GRB 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 Neutrinos t obs t obs [s] [s] GRB 5 Gamma rays Neutrinos t obs t obs [s] [s] MB, MURASE, WINTER, 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 ) GRB Gamma 3 rays Neutrinos t obs t obs [s] [s] Good ν emitter Good ν emitter Poor ν emitter GRB 6 Gamma rays Good ν emitter Poor ν emitter Poor ν emitter Neutrinos t obs t obs [s] [s] Gamma-ray, neutrino count [a.u] Gamma-ray, neutrino count [a.u] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17

24 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 ] subphotospheric extrap. multi-zone one-zone IC 2016 GRB limit E [GeV] GRB 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 ] E [GeV] GRB E [GeV] MB, MURASE, WINTER, GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] GRB E [GeV] GRB 6 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17

25 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 ] subphotospheric extrap. multi-zone one-zone IC 2016 GRB limit E [GeV] GRB 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 ] E [GeV] GRB E [GeV] MB, MURASE, WINTER, GRB 5 E 2 J νμ [GeV cm -2 s -1 sr -1 ] E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] GRB E [GeV] GRB 6 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17

26 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 ] IC GRB limit GRB GRB GRB subphotospheric extrap. multi-zone Good ν emitter one-zone Good ν emitter Poor ν emitter E [GeV] E [GeV] E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] GRB GRB GRB 6 Good ν emitter Poor ν emitter Poor ν emitter E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] MB, MURASE, WINTER, E 2 J νμ [GeV cm -2 s -1 sr -1 ] E [GeV] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 17

27 Time delays in gamma-ray light curves Neutrino-weak bursts show time delays in different energy bands Photon count [a.u.] GeV 80 Fermi-GBM GRB GeV Fermi-LAT GeV CTA t obs [s] MB, MURASE, WINTER, See also: BOŠNJAK, DAIGNE, A&A 568, A45 (2014) [ ] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 18

28 Time delays in gamma-ray light curves Neutrino-weak bursts show time delays in different energy bands Photon count [a.u.] GeV 80 Fermi-GBM GRB GeV Fermi-LAT GeV CTA t obs [s] MB, MURASE, WINTER, See also: BOŠNJAK, DAIGNE, A&A 568, A45 (2014) [ ] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 18

29 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

30 Backup slides Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 20

31 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

32 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 ( MeV = λ pγ erg s 1 Γ t v ε γ,break ) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 22

33 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? 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

34 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, (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 24

35 Neutrino spectra (at Earth) 10 7 Electron neutrino spectrum NeuCosmA Muon neutrino spectrum NeuCosmA 2010 E 2 Φ ΝeΝe GeV sr 1 s 1 cm Total flux Ν Μ WB flux Ν e E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm Total flux rescaled Total flux Ν e Ν Μ WB flux EGeV Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 25

36 Diffuse fluxes at Earth E 3 J CR GeV 2 cm 2 s 1 sr 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 f e 1 41 CR leakage dominated #2 f 1 e 62 Χ 2 d.o.f Neutrinos NeuCosmA 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

37 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 = typical values: t v = 10 s T 90 = 10 s N coll T 90 /t v 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

38 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 A 0.1 A Γ < 1 Speeds too similar, collisions only at large radii pdfk, A A 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

39 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

40 Tracking each collision individually Each collision occurs in a different emission regime R Ckm E 2 ΝΜ GeVcm2 neutrinos subphotospheric opt. thick to n's direct p escape R Ckm Ep,maxGeV cosmic rays UHECR 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

41 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

42 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

43 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

44 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 tchannel Multi Π WB approx. Higher resonances WB flux 1232 only neutrino flavor transitions Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 33

45 NeuCosmA the full photohadronic cross section 10 7 NeuCosmA 2010 E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm WB approx. WB flux Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34

46 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 WB approx. WB flux 1232 only P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34

47 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 WB approx. WB flux Higher resonances 1232 only P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34

48 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, (2011) E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm tchannel WB approx. Higher resonances WB flux 1232 only Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 34

49 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, (2011) E 2 Φ ΝΜΝΜ GeV sr 1 s 1 cm tchannel Multi Π WB approx. Higher resonances WB flux 1232 only 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

50 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

51 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 from Μ WB flux from n P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 35

52 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 WB flux from Π n p + e + ν e from K P. BAERWALD, S. HÜMMER, AND W. WINTER, Phys. Rev. D83, (2011) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 35

53 NeuCosmA how the neutrino spectrum changes I E Ν 2 F ΝEΝ GeV cm NeuCosmA ICFC RFC c fπ c s shape revised S. HÜMMER, P. BAERWALD, W. WINTER, Phys. Rev. Lett. 108, (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

54 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 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

55 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 bursts ν) 4π N GRB yr E Ν 2 Φ ΝE GeV cm 2 s 1 sr NeuCosmA 2012 IC40 IC4059 NFC prediction GRB, all GRB, z known stat. error astrophysical uncertainties f e 10 5 Flux 1 order of magnitude lower! IC86, 10y extrapolated S. HÜMMER, P. BAERWALD, W. WINTER, PRL 108, (2012) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 38

56 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 ) Ahlers et al. Waxman-Bahcall 90% 68% 50% Neutrino break energy εb (GeV) Exclusion CL (%) fp Standard 90% 50% 68% Γ Exclusion CL (%) [ICECUBE, ApJ 805, L5 (2015)] Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 39

57 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

58 We need direct proton escape Scan of the GRB emission parameter space acceleration efficiency η = 0.1 η = 1.0 LAT visible Η Η NeuCosmA Η 0.1Η z direct escape direct escape optically thick LAT invisible 800 no n escape at high efficiencies! NeuCosmA neutron escape optically thin to n escape optically thick to n escape LAT L Γ,iso ergs invisible 1 tvs full Σ pγ 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 Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 41

59 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

60 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

61 Cosmogenic neutrinos 10 6 E 2 JΝ all flavours GeV cm 2 s 1 sr IC diffuse UHE allflavor limit total interactions with CMB interactions with CIB NeuCosmA 2014 neutron decay P. BAERWALD, MB, W. WINTER, Astropart. Phys. 62, 66 (2015) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 43

62 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

63 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

64 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

65 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

66 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 log 10 R C km L peak γ R 2 C Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 45

67 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 a Γ 0=300, Γ = E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm b subphotospheric extrapolation evolving fireball IC40+59 stacking GRB limit standard numerical prediction Γ 0=500, Γ = E / GeV... and on the GRB engine variability time δt eng E 2 J νμ / GeV cm a subphotospheric extrapolation evolving fireball IC40+59 stacking GRB limit standard numerical prediction N sh=1000, N coll=794 δt eng =0.1s, t v=0.67s E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm b N sh=1000, N coll=457 δt eng =1.0s, t v=11.89s E / GeV -2 s -1 sr -1 E 2 J νμ / GeV cm -2 s -1 sr -1 E 2 J νμ / GeV cm c Γ 0=1000, Γ = E / GeV N sh=100, N coll=87-97 δt eng =0.1s, t v= s Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 46 c E / GeV

68 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: 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

69 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

70 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 ( erg) Shell speeds Γ k,0 follow a distribution (log-normal or other) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 49

71 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 ( 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

72 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 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

73 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 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) [ ] 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

74 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!" (!" )!" *!"!" +,-,$ $,-,,-,!" +!",-, +,-,!$" / ,.,!$"!"!!!" #!" $!" %!" &!" '!" (!" )!" *!"!" 4!,56178 I. TAMBORRA, S. ANDO, PRD 93, (2016) Mauricio Bustamante (CCAPP OSU) Multi-messenger GRB light curves 52