### Abstract

We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γ_{B}. In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η_{0} ∼ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η_{0}γ _{⊙} B in the direction of its initial bulk motion and with characteristic opening angle θ_{0} ∼ 1/γ_{B} . The flow is jet-like with Γθ_{0} ∼ 2η_{0} such that jets with Γ > 1/θ_{0} are naturally produced. The choice η_{0} ∼ γ_{B} ∼ 10 yields a jet with Γ ∼ 200 on-axis and angular structure characterized by opening angle θ_{0} ∼ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B ≳ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η_{0} and γ_{B} . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.

Original language | English (US) |
---|---|

Article number | L9 |

Journal | Astrophysical Journal Letters |

Volume | 776 |

Issue number | 1 |

DOIs | |

State | Published - Oct 10 2013 |

### Fingerprint

### Keywords

- gamma-ray burst: general
- hydrodynamics
- relativistic processes
- shock waves

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal Letters*,

*776*(1), [L9]. https://doi.org/10.1088/2041-8205/776/1/L9

**A "boosted fireball" model for structured relativistic jets.** / Duffell, Paul C.; Macfadyen, Andrew I.

Research output: Contribution to journal › Article

*Astrophysical Journal Letters*, vol. 776, no. 1, L9. https://doi.org/10.1088/2041-8205/776/1/L9

}

TY - JOUR

T1 - A "boosted fireball" model for structured relativistic jets

AU - Duffell, Paul C.

AU - Macfadyen, Andrew I.

PY - 2013/10/10

Y1 - 2013/10/10

N2 - We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γB. In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η0 ∼ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η0γ ⊙ B in the direction of its initial bulk motion and with characteristic opening angle θ0 ∼ 1/γB . The flow is jet-like with Γθ0 ∼ 2η0 such that jets with Γ > 1/θ0 are naturally produced. The choice η0 ∼ γB ∼ 10 yields a jet with Γ ∼ 200 on-axis and angular structure characterized by opening angle θ0 ∼ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B ≳ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η0 and γB . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.

AB - We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γB. In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η0 ∼ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η0γ ⊙ B in the direction of its initial bulk motion and with characteristic opening angle θ0 ∼ 1/γB . The flow is jet-like with Γθ0 ∼ 2η0 such that jets with Γ > 1/θ0 are naturally produced. The choice η0 ∼ γB ∼ 10 yields a jet with Γ ∼ 200 on-axis and angular structure characterized by opening angle θ0 ∼ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B ≳ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η0 and γB . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.

KW - gamma-ray burst: general

KW - hydrodynamics

KW - relativistic processes

KW - shock waves

UR - http://www.scopus.com/inward/record.url?scp=84884861268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884861268&partnerID=8YFLogxK

U2 - 10.1088/2041-8205/776/1/L9

DO - 10.1088/2041-8205/776/1/L9

M3 - Article

VL - 776

JO - Astrophysical Journal Letters

JF - Astrophysical Journal Letters

SN - 2041-8205

IS - 1

M1 - L9

ER -