Light Curves and Inner Engines Tsvi Piran HU, Jerusalem

Transcription

1 Light Curves and Inner Engines Tsvi Piran HU, Jerusalem Theory and observations of Light curves Ehud Naker Implication of accretion theory P. Kumar & R. Narayan counts/sec x Time since trigger (sec) TP Sackler 5/00 1

2 The Internal-External Fireball Model γ-rays Afterglow Inner Engine Relativistic Wind Internal Shocks External Shock There are no direct observations of the inner engine. The γ-rays light curve contains the best evidence on the inner engine s s activity.

3 1) Gamma-Ray Light Curves: A Reflection of GRBs Inner Engines Ehud Nakar & TP Variability Internal shocks. Observations of Gamma-Rays light curve. Similarity between pulse width and intervals. A correlation between intervals and consecutive pulses. 3. An internal shocks toy model. 4. Implications for the inner engine.

4 Highly variable signal Internal Shocks (Sari & Piran 97) For external shocks: t ang ~ t rad ~R/c ~R/cγ (Fenimore et al. 96, Sari & Piran, 97). < t rad (hydrodynamics considerations) The covering factor and hence the efficiency will be <<1, if the angular size of the emitting regions is significantly smaller than γ. counts/sec x Time since trigger (sec) C R θ~1/ ~1/γ D A R R B

5 For External Shocks Expect different behavior earlier (Larger γ) and later (Lower γ) during the burst. Ηowever, Fenimore & Ramirez-Ruiz (00) show that the early pulses and later pulses are similar! counts/sec x Time since trigger (sec) TP Sackler 5/00 5

6 Internal Shocks =ct = R/c R /c /c=t =c T The observed light curve reflects the activity of the inner engine. fi Need TWO time scales. T δt TP Sackler 5/00 6

7 An Important Remark The internal shocks model is essential only for variable GRBs. Smooth GRBs (~15% of the bursts) can be produced by external shocks. TP Sackler 5/00 7

8 Light Curves Observations (Nakar & TP 001) t and δt have similar distributions (once we delete long quiescent periods from the intervals distribution). Counts/sec x 10 4 δt t Time (sec) Dt histogram dt histogram t (sec) δt (sec)

9 Quiescent Periods TP Sackler 5/00 9

10 An interval, t i, and its consecutive pulse, δt i, are correlated. TP Sackler 5/00 10

11 Numerical simulations Kobayashi, TP & Sari 1997; Daigne & Mochkovitch 1997; Spada et. al Shell ejection time Pulse observed time 1 The observed light curve reflects the temporal behavior of the `inner engine.

12 The model should explain: The similarity of the t and δt distributions. The t - δt correlation. The reflection of the `inner engine activity in the light curve.

13 An Internal Shocks Toy Model Discrete shells: -well defined Lorentz factors. -well defined boundaries. γ γ 1 Collision pulse Collided shells are merged -merged shell parameters are obtained by momentum and energy conservation.

14 A single collision a = γ > γ 1 1 γ = γ γ = aγ l L 1, 1 l 1 t + + t l L 1 1 1, t t1 Collision efficiency (for equal mass shells): ε = 1 a a + 1 For a reasonable efficiency (>5%): a >

15 γ >>1 β = 1 γ 1 Collision radius: a > Collision observed time (photon t obs R c (photon s s flying time to the observer omitted): = = t 1 β + 1 L l 1 1, β + R c 1 γ γ L1, γ L 1, a a 1 1 a ( β 1) t1 + l1 + L1, a 1 t obs t 1 + l1 + L1, t γ = γ 1 γ = aγ t obs reflects the emission time, t, of the inner fast shell. l L 1, l 1 t t1

16 The Pulse Width* Dominant time scales: Angular time: 1/γ B A t ang = t B t A R s /(γ sh ) g sh is the Lorentz factor of the shocked region Hydrodynamic time: B A t hyd = t B t A l * Assuming t cool << t ang δt γ t + t L + ang hyd γ sh TP Sackler 5/00 16 l

17 Three Types of Multiple collisions* l L l 1 1, t t 1 Type I: t t 4 t l + L,3 + l 3 + L 3,4 δt l 4 + L 3,4 Type II: t t 3 t l + L,3 δt l 3 + L,3 * All multiple collisions can be composed of those three types.

18 Type I & II Collisions: Variable light curve. Dt and dt are governed by the same `inner engine` parameters. For equal energy: Dt i ~ dt i ~ L i,i+1 Reflect the `inner engine temporal activity. TP Sackler 5/00 18

19 Type III: t < δt The two pulses overlaps and are observed as a single pulse. Type III Collisions: Not variable. No Dt- dt similarity. Do not reflect the `inner engine temporal activity.

20 t 4 t t 5 Type I Type II t 5 Type III TP Sackler 5/00 0

21 Numerical Simulations Goals: Determine the fraction of types I & II collisions. Validate the assumptions of the analytic toy model. Assumptions: Discrete shells. Shells merge after a collision TP Sackler 5/00 1

22 t 4 t t 5 Type I Type II t 5 Type III TP Sackler 5/00

23 # of collisions / # of ejected shells ε Collisions types Equal mass > Type % of the efficient collisions are types I & II. Equal energy shells => type II is dominant. Equal mass shells => type I is dominant Equal energy ε >0.05 Type TP Sackler 5/00 3

24 Dt and dt distributions Fraction of events Equal mass a) b) δt t L Equal energy δt t L time(sec) time(sec) The equal energy model fits the observations very well. In the equal mass model the pulses are much narrower than the intervals. TP Sackler 5/00 4

25 t(sec) δt(sec) µ 1σ µ 1σ Simulations Observations δt t δt t TP Sackler 5/00 5

26 Summary (part 1) Each pulse reflects the ejection time of the inner shell The light curve reflects the inner engine s s activity. The intervals between pulses and the duration of the pulses (for the equal energy model) reflect the shells initial separation (Dt ~ dt ~ L/c). The observed similarity and correlation arise naturally in internal shocks with equal energy shells (mass modulation of constant energy flow) Simple internal shocks with equal mass shells do not fit the observations.

27 Implications to the Source Need two (three?) different time scales. Pulse properties do not change along the burst. Possible energy sources: Accretion χ Long time scale accretion time Short time scale Instability, dynamical time of the system. Rotation The source slows down as it relases energy must find an explanation for above. TP Sackler 5/00 7

28 Recent progress in accretion theory (see e.g., Igumenshchev, Abramovich,, & Narayn) In CDAF (Convection dominated accretion flow) most of the matter is ejected back to infinity at slow velocities (Blandford( & Beegelman,, 99) accretion efficiency is very low. Simulations of 3D accretion Igumenshchev Abramowicz & Narayan Accretion is effective in NDAF (Neutrino dominated accretion flow) (Popham( Popham, Woosley & Fryer, 01). TP Sackler 5/00 8

29 ) Accretion theory and models of the Inner Engine: R. Narayan TP & Kumar Most GRB models are based on accretion onto a black hole. Davies et al, NS merger, MacFadyen & 94 Woosley, Collapsar, 00 TP Sackler 5/00 9

30 Contours of Log(t acc ) -1 1 ACCRETION TIME Burst Duration optically thick to neutrinos NDAF CDAF t acc is determined by the size of the disk. Disk mass in units of m o CDAF to NDAF gas-pressure-dominated to degeneracy -dominated Disk size in units of r g TP Sackler 5/00 30

31 Implications I Need large disks ( r g ) to produce long duration bursts. Need small disks (10r g ) to produce short bursts. TP Sackler 5/00 31

32 Accretion Efficiency Need ergs m acc acc M. O Define x as the ratio between the disk mass m d and the mass that is actually accreted onto the black hole m acc : x m acc / m d. Note that overall efficiency is even smaller as not all of m acc is converted to energy. TP Sackler 5/00 3

33 Contours of Log(x) ) - Accretion efficiency Optically thick to neutrinos- low efficiency of conversion to radiation (Dimatteo, Perna, Narayan, 0) NDAF x=1 ξ m acc md CDAF Disk mass in units of m o x=.1 Disk size in units of r g TP Sackler 5/00 33

34 Time Scales: Implications II Need large disks ( r g ) to produce long duration bursts. Need small disks (10r g ) to produce short bursts. Efficiency: MLarge disks ( r g ) are inefficient and cannot produce ergs.??? Small disks (10r g ) are efficient. TP Sackler 5/00 34

35 MLarge disks ( r g ) are inefficient and cannot produce ergs.??? Consider another possibility: accretion+mass injection. Injection of mass onto a small disk by infall Collapsar (MacFadyen & Woosley,, 01) Disk is fed by infall over a long time scale Small accretion disk (high efficiency) TP Sackler 5/00 35

36 Contours of Log(x) ) - Accretion efficiency NDAF x=1 CDAF Accretion rate in units of m o /sec x=.1 Disk size in units of r g TP Sackler 5/00 36

37 Summary (part ) Large CDAFs are inefficient. Models with large accretion disks (He star NS/BH; WD-NS/BH; etc..) are ruled out. A Collapsar might produce a small NDAF disk. The long duration arises from the long infall time and NOT by the accretion time. NS mergers produce small NDAF disks in which the duration is determined by the accretion time. TP Sackler 5/00 37

38 Routes to a BH-Disk-Jet Different routes can lead to a Black-hole -disk-jet system: NS/BH-NS merger - SHORT BH-WD merger NS/BH-He core merger Collapsar - LONG short Long Davies et al, 94 Woosley et al, 99 TP Sackler 5/00 38

39 Roswog et al, 99 TP Sackler 5/00 39 Woosley et al., 99

40 SUMMARY The Internal shocks mechanism: GRB light curves reproduce the activity of the inner engines. The inner engines modulate of the wind s s mass within a constant energy flow. Quiescent periods long periods in which the inner engine is inactive. The time scales and the internal shocks mechanism suggest that the sources are based on accretion onto a black hole. TP Sackler 5/00 40

41 Small disks can produce efficiently short bursts. Large disks are very inefficient. To poduce long bursts need infall onto a small disk. Long bursts are produced by Collapsars. Short bursts are produced by mergers. TP Sackler 5/00 41

42 Clumpy ISM Efficiency ~ 10% for δt/t~0.01 With 30% modulation (Dermer & Mitman, 99) However: 4 Many bursts show δt / T ~ 10 (Nakar & Piran 001) Quiescent periods are impossible with this efficiency. t is governed by the angular separation between the clumps, and the clumps location. δt is governed by the clumps size and viewing angle (later pulses should be wider). Contradict the observations (Fenimore & Ramirez-Ruiz 000). No reason for t-δt similarity and correlation. TP Sackler 5/00 4

43 Shot-Gun Model t is governed by activity of the inner engine δt is governed by properties of the circumburst matter No reason for t-δt similarity and correlation. TP Sackler 5/00 43