1. Orphan Afterglows Daniel Perley Astro 250 3 April 2007

2. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Gamma-Ray Burst Review Burst of gamma-ray emission lasting 0.01 – 1000 s Typical fluence 10 -7 to 10 -3 erg/cm 2 Isotropic (extragalactic); 0.01 < z < 7 Observed rate ~1-3/day Less for instruments with limited sensitivity or field of view Followed by long-wavelength afterglow counterpart Lasts for days to weeks to months GRB Review

3. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows GRB vs. Afterglow GRB Review GRB: Internal ShocksAfterglow: Forward Shock Collision/interaction of shells of ultra-relativistic ejected material Intrinsic to progenitor Relativistic shock moving into circumburst medium Depends on environment

4. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows GRBs are Relativistic GRBs have short-timescale structure → small GRBs are extremely distant → extreme energy density Very large photon densities result in pair production (  → e + e - ) opacity But, Spectrum is non-thermal Extremely high-energy photons observed for some bursts Solution: relativistic motion towards observer (energy density in source frame can be much less due to Doppler/light-travel/relativistic effects) "compactness problem" GRB Review

5. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows GRBs are Anisotropic... probably Isotropic-derved energy requirements are phenomenal GRB971214 (z=3.42) : E iso = 2.1 × 10 53 erg GRB990123 (z=1.60) : E iso = 1.4 × 10 54 erg GRB050904 (z=6.29) : E iso = 3.8 × 10 53 erg E iso ≡ (S  ) × 4 π d L 2 M. c 2 = 1.78 × 10 54 erg gamma-rays only Most theoretical models favor jet geometry GRB Review

6. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows GRB Jets Assume that GRBs are jetted. Fairly good evidence this is the case. Recently the details are becoming controversial again. How does a jet geometry affect the appearance and evolution of a GRB and its afterglow? GRB Jets

7. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows The Relativistic Beam An emitter moving at v ~ c, even if emitting isotropically in its rest frame, will strongly beam its radiation as seen by the observer. GRB Jets v = 0 Γ = 1 v ~ c Γ >> 1 Beaming angle : Ω = 4π Beaming angle : Ω = π θ 2 θ beam ~ 1 / Γ 1 / Γ

8. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Prompt Emission Beaming Initially, the GRB emission is strongly beamed towards the observer. (and anyone else within the jet beam) θ jet intrinsic burst parameters: θ jet - jet opening angle E iso - 4π × energy per steradian Γ init – initial Lorentz factor Assume for simplicity a uniform ("top-hat") jet throughout this analysis. θ beam = 1 / Γ init internal shocks (prompt) t = 10 sec Γ init we see only a small part of the emitting region GRB Jets

9. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Afterglow Beaming Once the afterglow sets in, the shock has swept up significant quantities of circumburst material and is decelerating. external shock θ beam = 1 / Γ Γ θ jet t = 100 sec GRB Jets

10. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Afterglow Beaming Each part of the afterglow shock is therefore beaming its emission into a larger area. t = 100 sec Γ θ jet θ beam = 1 / Γ GRB Jets

11. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Afterglow Beaming the apparent emitting region becomes a larger fraction of the jet (specifically, θ E = θ beam = 1/Γ) 1 / Γ Each part of the afterglow shock is therefore beaming its emission into a larger area. t = 100 sec Γ θ jet GRB Jets However, this does not affect the flux viewed from Earth: emission from other areas is now beamed in our direction, replacing the lost flux.

12. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Jet Break Eventually, the shock slows down enough that the apparent emitting region is the entire jet. t = 1 day Γ θ jet Note that up until this point, the GRB evolution is indistinguishable from a spherical explosion – points outside the jet are out of causal contact. Occurs when θ E = θ jet 1/Γ = θ jet Γ = 1/θ jet GRB Jets

13. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Post-Jet Break Evolution After this point, the increasingly outward-beamed radiation is no longer compensated by seeing more of the jet, and the observed flux drops rapidly. θ jet Γ t = 10 day GRB Jets

14. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Sideways Spreading At about the same time, the jet itself becomes "aware" of its finite extent, and it begins to expand outward. Its forward motion rapidly decelerates. t = 100 day Γ Γ ~ e -r/r sedov ~ t -1/2 GRB Jets

15. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Transition to Non-Relativistic Eventually the shock becomes nonrelativistic and unbeamed. Γ ~ 1 t = 500 day GRB Jets

16. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Jet Light Curves Quantitative predictions are somewhat in dispute... log F log t t -(3/4)(p-1) t -(3/4)p t -p log F t jet t 1/2 t -1/3 t -9/10 const t -1/4 ? optical / x-ray radio t jet t spread t NR Generally agreed-upon predictions: First break occurs when Γ = 1/θ jet Hydrodynamics: Γ(t) ~ 6 (E iso /n ISM ) 1/8 t -3/8 t jet ~ 0.25d (E/n) 1/3 (θ jet /0.1) 8/3 Break should be achromatic No change in the spectrum; just viewing geometry E iso in units of 10 52 erg n ISM in units of cm -3 t in units of day GRB Jets

17. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Observed Jet Breaks Jet breaks have been seen. Maybe. GRB 030226 If the Swift jet break crisis is real, all of this may be bunk. still unbroken at 15 days GRB Jets

18. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Off-Axis Prompt Emission What if the jet is not directed at us? θ jet Γ init GRB emission is completely absent outside the physical jet beam (the relativistic beam is much narrower at this stage) Off-Axis Jets θ beam = 1 / Γ init

19. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Off-Axis Early Afterglow The early afterglow is also invisible. θ jet Γ Off-Axis Jets

20. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Off-Axis Jet Break Sometime after the "break" time, however, the jet becomes visible θ jet Jet center is visible when θ beam ~ θ obs Γ(t) ~ 1/θ obs θ obs Γ Once the full jet is visible the afterglow will be (about) as bright as if we were on-axis at this time Off-Axis Jets

21. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Off-Axis Light Curves Off-axis light curve similar to on-axis, except that there is nearly no flux until Γ(t) ~ 1/θ obs log F t -(3/4)(p-1) t -(3/4)p t -p optical / x-ray log t log F t jet t 1/2 t -1/3 const t -1/4 ? radio t spread t NR Off-Axis Jets There is an afterglow without a GRB: "orphan afterglow"

22. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Off-Axis Light Curves Some more precise predictions: Radio (Totani & Panaitescu 2000) Optical (Granot et al. 2002) Off-Axis Jets

23. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Another Pathway: Dirty GRBs One can also generate an on-axis orphan afterglow by surpressing the GRB (gamma-ray) flux. This can be achieved with an energetic but low-Γ init burst outflow: will be opaque to pair-production (remember compactness problem) and not generate gamma rays, but will create a "normal" afterglow. Γ init Dirty GRBs I will ignore this completely in the remainder of the lecture.

24. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows The Orphan Afterglow Rate For any burst, the post-jet afterglow is beamed towards a much larger angle than the early afterglow, so the rate of orphan afterglows should be very large. θ obs Typically, θ jet ~ 5° θ obs potentially can be the whole sky θ jet However, GRBs are much brighter and easier to detect than orphan afterglows, and can be seen to much greater distances / less energetic events. The Orphan Afterglow Rate

25. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Afterglow Rate Estimate Procedure Intrinsic questions: What is the GRB rate as a function of redshift? What is the GRB luminosity function? What is the jet angle distribution? What is the distribution of Γ init and n ISM ? How does afterglow luminosity relate to GRB luminosity? Survey questions: What is the survey sky area? What is the survey flux limit? Can the survey distinguish OAs from other transients? The Orphan Afterglow Rate

26. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Optical Orphan Afterglow Rate Optical orphan afterglows: "near misses" Optical Orphan Afterglow Rate Optical flux drops precipitously after the jet break (the soonest possible time an off-axis afterglow can be observed) Therefore, only near-axis events will be seen. But these events can be quite bright and visible to large (cosmological) distances: intrinsic luminosity limited.

27. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows A First-Cut Estimate Rate of GRBs: 1000 / year Fraction of GRBs with afterglow detectable (R<23) to t ~ 10 t jet : 3% Observable for ~10 days For an R<23 survey: # on-axis detectable afterglows: 30 / sky / year = 1 / sky now # off-axis afterglows: 3 2 this many 300 /sky/year = 10 / sky now Need to survey the equivalent of 1/10 of the sky (4000 sq deg.) to find an orphan afterglow. Can repeat if the interval is >~ 10 days. Optical Orphan Afterglow Rate

28. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows More Precise Estimates Estimates in the literature vary wildly. Uncertain rate of very low-luminosity GRBs Uncertainty in actual light curve of an off-axis event Uncertain distribution of GRB afterglow luminosities (dark bursts, etc) Totani & Panaitescu (2002) Zou et al. (2007) Nakar et al. (2002) Optical Orphan Afterglow Rate

29. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Optical Survey Design Shallow and wide, or narrow and deep? Totani & Panaitescu (2002) Zou et al. (2002) Nakar et al. (2007) but, expect R  F -1 → shallow survey limiting flux of a telescope: F limit  t exp -1/2 t exp  F limit -2 area of a survey : A survey = (T survey / t exp ) × FOV  t exp -1  F limit 2 limiting rate of a survey: R limit = 4π/A survey ~ F limit -2 Hypothetical Lick survey Optical Orphan Afterglow Rate

30. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Radio Orphan Afterglow Rate Radio orphan afterglows: low-z GRB remnants Radio emission most easily detected during late (non-relativistic, ~isotropic) stage of GRB evolution. Intrinsic energy output is ~constant (~10 51 erg). → Late-time radio luminosity should also be constant: radio OA's are distance-limited.

31. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows A First-Cut Estimate Rate of GRBs: 1000 / year Observable for ~1 year ~1000 x number of current optical afterglows 970508: 70 μJy at 250 days (8 GHz) z = 0.835 VLA sensitivity limit: 50 μJy in 10 min ~20% of GRBs are at z < 1 → 200 detectable on-axis radio afterglows / sky / yr 200 × 100 = 20,000 detectable radio afterglows / sky / yr 20,000 detectable radio afterglows / sky now Radio Orphan Afterglow Rate Frail et al. 2000

32. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows More Precise Estimates Also variable; depends on low-z GRB rate, beaming fraction, and ISM density F lim (μJy) 10 10.11001000 10 3 10 4 10 5 10 6 10 7 N (F > F lim ) N R ~ 20 (f  / 5 mJy) -3/2 Levinson et al. 2002 Radio Orphan Afterglow Rate Levinson et al. 2002

33. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Radio Survey Design Wide or deep? F lim (μJy) 10 10.11001000 10 3 10 4 10 5 10 6 10 7 N (F > F lim ) limiting rate of a survey: R limit = 4π/A survey  F limit -2 Hypothetical VLA survey expect R  F -3/2 → wide/shallow Radio Orphan Afterglow Rate

34. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Real Surveys Searches for long-wavelength high-z transients are still in their early stages. Some preliminary results: FIRST / NVSS Bower survey CFHT-WF survey Many others I am ignoring Upcoming surveys: ATA, SDSS, Pan-STARRS, LSST, SKA Orphan Afterglow Surveys

35. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows NVSS-FIRST Transient Search Comparison of two VLA wide-field radio surveys (FIRST, NVSS) FIRST: Galactic caps, 3 minute integrations, 21 cm, B-configuration (5" resolution) NVSS: Entire northern sky, 21 cm, D-configuration (45" resolution) F lim ~ 5 mJy A survey ~ 2400 sq. deg Two epochs, variable interval 9 transient candidates identified 1 radio supernova, others not identifiable (lack of information) No orphan afterglows detected (survey sensitivity is low; any OA would be coincident with a bright galaxy) θ jet < 15° Orphan Afterglow Surveys

36. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Bower Transient Survey 22-year, extensively repeated survey of a blank field in far northern sky 5-8 GHz F lim ~ 500 μJy A ~ 0.02 sq. deg 944 epochs A eff ~ 10 sq.deg 10 transients detected 1 probable radio supernova 1 radio supernova or GRB afterglow (orphan or otherwise) 8 unknown sources Orphan Afterglow Surveys

37. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows CFHTLS-VWS Canada France Hawaii Telescope Legacy Survey (Very Wide Survey) A ~ 490 sq. deg m lim = 22.5 (r' - band) 14 epochs 1067 transients 1066 variable stars / asteroids / KBOs 1 orphan afterglow candidate Orphan Afterglow Surveys Malacrino et al. 2007

38. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Other Surveys Totani & Panaitescu 2002 Orphan Afterglow Surveys

39. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows Pan-STARRS and LSST Extremely wide, deep future optical surveys Pan-STARRS PS1 1.8m telescope, FOV of 7 sq. deg. Entire visible sky to R~23 each week OA rate ~ 100 / year Completion 2007 PS4 2.2m telescope, FOV of 28 sq. deg? 1 OA per day? LSST Large Synoptic Survey Telescope 8.4m telescope, FOV 3.5 sq. deg Entire visible sky to R~24 in 3 nights OA rate ~ many / night Completion 2012? Future Surveys

40. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows ATA and SKA Upcoming radio instruments ATA Allen Telescope Array 4 sq. deg FOV Visible sky to 1 mJy each week OA rate ~ 1 / night Future Surveys SKA Square Kilometer Array Large telescope to be completed in effectively indefinite future Many times ATA transient rate

41. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows The Future The future for these orphans may not be so grim after all! Future Surveys

42. Daniel Perley 3 April 2007Astro 250: Orphan Afterglows F limit ~ t exp 1/2 m limit ~ m lim,o + 2.5 × (1/2) * log 10 (t exp ) t exp = t o × 10 (m limit -m lim,o )/1.25 A survey = (T survey / t exp ) × FOV = (T survey / 1 hr × 10 (m limit -23)/1.25 ) × FOV = (2000 × 10 (m limit -23)/1.25 ) × 0.1 sq. deg = (200 sq. deg) × 10 (m limit -23)/1.25 4π/A survey = 200 × 10 -(m limit -23)/1.25 log R lim ~ -5/4 m