Jet Models of X-Ray Flashes D. Q. Lamb (U. Chicago) Triggering Relativistic Jets Cozumel, Mexico 27 March –1 April 2005

Density of HETE-2 Bursts in (S, E peak )-Plane “Global Properties of XRFs and X-Ray-Rich GRBs Observed by HETE-2” Sakamoto et al. (2005; astro-ph/ )

Relation Between Spectral Peak Energy (E peak ) and Isotropic Radiated Energy (E iso )  Found by BeppoSAX for GRBs (Amati et al. 2002)  Confirmed for GRBs and extended to XRFs by HETE-2 (Sakamoto et al. 2004; Lamb et al. 2004)  Relation spans five decades in E iso GRB GRB GRB

Time-Resolved Spectra of BATSE Bursts Obey L iso -E peak Relation Liang et al. (2004)

BATSE Bursts Without Known Redshifts Obey L iso -E peak Relation Redshift estimated from star formation rate (Liang and Dai 2004) Redshift estimated from spectral lag (Ghirlanda et al. 2005)

Implications of HETE-2 Observations of XRFs and X-Ray-Rich GRBs qHETE-2 results, when combined with earlier BeppoSax and optical follow-up results: q Provide strong evidence that properties of XRFs, X-ray-rich GRBs (“XRRs”), and GRBs form a continuum q Key result: approximately equal numbers of bursts per logrithmic interval in all observed properties q Suggest that these three kinds of bursts are closely related phenomena

Scientific Importance of XRFs  As most extreme burst population, XRFs provide severe constraints on burst models and unique insights into  Structure of GRB jets  GRB rate  Nature of Type Ic supernovae  Some key questions regarding XRFs:  Is E gamma (XRFs) << E gamma (GRBs)?  Is the XRF population a direct extension of the GRB and X-Ray-Rich GRB populations?  Are XRFS a separate component of GRBs?  Are XRFs due to different physics than GRBs and X-Ray Rich GRBs?  Does burst population extend down to UV (and optical)?

Physical Models of XRFs qX-ray photons may be produced by the hot cocoon surrounding the GRB jet as it breaks out and could produce XRF-like events if viewed well off axis of jet (Meszaros et al. 2002, Woosley et al. 2003). q“Dirty fireball” model of XRFs posits that baryonic material is entrained in the GRB jet, resulting in a bulk Lorentz factor Gamma > 300 and the contrast between the bulk Lorentz factors of the colliding relativistic shells are small can also produce XRF-like events (Mochkovitch et al. 2003). qA highly collimated GRB jet viewed well off the axis of the jet will have low values of E iso and E peak because of the effects of relativistic beaming (Yamazaki et al. 2002, 2003, 2004). qXRFs might be produced by a two-component jet in which GRBs and XRRs are produced by a high-Gamma core and XRFs are produced by a low-Gamma “halo” (Huang et al. 2004).

Phenomenological Jet Models Universal ● Power-Law Jet ● Fisher Jet Diagram from Lloyd-Ronning and Ramirez-Ruiz (2002) Variable Opening-Angle (VOA) ● Uniform Jet ● Fisher Jet ● VOA Uniform Jet + Relativistic Beaming ● Core + Halo Jet

Determining If Bursts are Detected HETE-2 burstsBeppoSAX bursts DQL, Donaghy, and Graziani (2004)

Variable Opening-Angle Uniform Jet Versus Universal Power-Law Jet DQL, Donaghy, and Graziani (2004) Variable opening-angle (VOA) Universal power-law jet uniform jet

Variable Opening-Angle Uniform Jet Versus Universal Power-Law Jet  VOA uniform jet can account for both XRFs and GRBs  Universal power-law jet can account for GRBs, but not both XRFs and GRBs DQL, Donaghy, and Graziani (2004)

Universal Gaussian Jet  In response to conclusion of DQL, Donaghy, and Graziani (2004), Zhang et al. (2004) proposed universal Gaussian jet  Universal Gaussian jet  can produce ~ equal numbers of bursts per logarithmic interval  requires minimum theta jet ~ 2 o as does VOA uniform jet Zhang et al. (2004)

Universal Versus VOA Fisher Jets Donaghy, Graziani and DQL (2004) Universal Fisher jet w. minimum theta jet = 2 o VOA Fisher jet w. minimum theta jet = 2 o

Universal Versus VOA Fisher Jets Donaghy, Graziani and DQL (2004) VOA Fisher jetUniversal Fisher jet  Peak of E gamma inf ~ 5 times smaller than actual value  E gamma inf distribution has low-energy tail (of XRFs)

Fisher Jet Models qWe have shown mathematically that universal jet with emissivity given by Fisher distribution (which is natural extension of Gaussian distribution to sphere) has the unique property of producing equal numbers of bursts per logarithmic interval in E iso and therefore in most burst properties qUniversal and VOA Fisher jets can reproduce most burst properties qBoth models require minimum theta jet ~ 2 o, similar to VOA uniform jet qBoth produce a broad distribution in inferred radiated gamma-ray energy E gamma inf, in contrast with VOA uniform jet

VOA Uniform Jet + Relativistic Beaming Yamazaki et al. (2004)Donaghy (2004)

Structured (Core + Halo) Jet Models Huang et al. (2004)  It is not clear in such a model  why properties of XRFs, XRRs, and GRBs form a continuum  why there are ~ equal numbers of XRFs, XRRs, and GRBs

VOA Uniform Jet + Relativistic Beaming  Relativistic beaming produces low E iso and E peak values when uniform jet is viewed outside theta jet (see Yamazaki et al. 2002, 2003, 2004; Donaghy 2004)  Relativistic beaming must be present  Therefore very faint bursts w. E peak obs in UV and optical must exist  However, key question is whether this effect dominates  Yamazaki et al. (2004) use VOA uniform jet for XRRs and GRBs, relativistic beaming for XRFs  If Gamma ~ 100, XRFs produced by relativistic beaming are detectable; but if Gamma ~ 300, very few are detectable => may be difficult to produce ~ equal numbers of XRFs, XRRs, and GRBs

X-Ray Flashes vs. GRBs: HETE-2 and Swift (BAT) GRB Spectrum Peaks in Gamma - Rays XRF Spectrum Peaks in X-Rays Even with the BAT’s huge effective area (~2600 cm 2 ), only HETE-2 can determine the spectral properties of most bursts, especially XRFs

Conclusions  HETE-2 has provided strong evidence that XRFs, “X-ray-rich” GRBs, and GRBs are closely related phenomena  XRFs provide unique information about q structure of GRB jets q GRB rate q nature of Type Ic SNe qExtracting this information will require prompt q localization of many XRFs q determination of E peak q identification of X-ray and optical afterglows q determination of redshifts qHETE-2 is ideally suited to do the first two, whereas Swift (with 15 < E < 150 keV) is not; Swift is ideally suited to do the second two, whereas HETE-2 cannot qPrompt Swift XRT and UVOT observations of HETE-2 XRFs can therefore greatly advance our understanding of XRFs