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, Epeak)-Plane

“Global Properties of XRFs and X-Ray-Rich GRBs Observed by HETE-2” Sakamoto et al. (2005; astro-ph/0409128)

Relation Between Spectral Peak Energy (Epeak) and Isotropic Radiated Energy (Eiso)

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 Eiso

GRB 980425

GRB 031203

GRB 050401

Time-Resolved Spectra of BATSE Bursts Obey Liso-Epeak Relation

Liang et al. (2004)

BATSE Bursts Without Known Redshifts Obey Liso-Epeak Relation

Redshift estimated from star formation rate (Liang and Dai 2004) Redshift estimated from

spectral lag (Ghirlandaet al. 2005)

Implications of HETE-2 Observations of XRFs and X-Ray-Rich GRBs

HETE-2 results, when combined with earlier BeppoSax and optical follow-up results:Provide strong evidence that properties of XRFs,

X-ray-rich GRBs (“XRRs”), and GRBs form a continuum

Key result: approximately equal numbers of bursts per logrithmic interval in all observed properties

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 Egamma (XRFs) << Egamma (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

X-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).

“Dirty fireball” model of XRFs posits that baryonic material is entrained in the GRB jet, resulting in a bulk Lorentz factor Gamma << 300 (Dermer et al. 1999, Huang et al. 2002, Dermer and Mitman 2003). At opposite extreme, GRB jets in which the bulk 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).

A highly collimated GRB jet viewed well off the axis of the jet will have low values of Eiso and Epeak because of the effects of relativistic beaming (Yamazaki et al. 2002, 2003, 2004).

XRFs 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 thetajet ~ 2o as does VOA uniform jet

Zhang et al. (2004)

Universal Versus VOA Fisher Jets

Donaghy, Graziani and DQL (2004)

Universal Fisher jet w.minimum thetajet = 2o

VOA Fisher jet w.minimum thetajet = 2o

Universal Versus VOA Fisher Jets

Donaghy, Graziani and DQL (2004)

VOA Fisher jetUniversal Fisher jet

Peak of Egammainf ~ 5 times smaller than actual value

Egammainf distribution has low-energy tail (of XRFs)

Fisher Jet Models

We 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 Eiso and therefore in most burst properties

Universal and VOA Fisher jets can reproduce most burst properties

Both models require minimum thetajet ~ 2o, similar to VOA uniform jet

Both produce a broad distribution in inferred radiated gamma-ray energy Egamma

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 Eiso and Epeak values when uniform jet is viewed outside thetajet (see Yamazaki et al. 2002, 2003, 2004; Donaghy 2004) Relativistic beaming must be present

Therefore very faint bursts w. Epeakobs 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: X-Ray Flashes vs. GRBs: HETE-2 and HETE-2 and SwiftSwift (BAT) (BAT)

GRB SpectrumPeaks in Gamma - Rays

XRF Spectrum Peaks in X-Rays

Even with the BAT’s huge

effective area (~2600 cm2), 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

structure of GRB jets GRB rate nature of Type Ic SNe

Extracting this information will require prompt localization of many XRFs determination of Epeak

identification of X-ray and optical afterglows determination of redshifts

HETE-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

Prompt Swift XRT and UVOT observations of HETE-2 XRFs can therefore greatly advance our understanding of XRFs