[Paper Review] Internal shocks model for microquasar jets

Omar Jamil, R. P. Fender+1 more|ArXiv.org|Nov 20, 2008

Astrophysics and Cosmic Phenomena8 references3 citations

TL;DR

This paper proposes an internal shocks model for microquasar jets, where discrete, variable-speed ejecta (shells) collide to produce shocks that accelerate particles and generate radiation via synchrotron emission. The model reproduces flat radio-IR spectra by balancing energy dissipation, adiabatic losses, and optical depth evolution, with key results showing that shell mass, Lorentz factor differences, and ejection frequency critically shape lightcurves and spectral energy distributions.

ABSTRACT

We present an internal shocks model to investigate particle acceleration and radiation production in microquasar jets. The jet is modelled with discrete ejecta at various time intervals. These ejecta (or 'shells') may have different properties including the bulk velocity. Faster shells can catch up and collide with the slower ones, thus giving rise to shocks. The particles are accelerated inside the shocked plasma. Each collision results in a new shell, which may take part in any subsequent collisions as well as radiate due to synchrotron radiation. Almost continuous energy dissipation along the jet can be obtained with a large number of shell collisions. We investigate the spectral energy distribution of such jets as well as the physical significance of various parameters (e.g. the time interval between ejections and the shell size).

Motivation & Objective

• To explain the origin of flat radio spectra in microquasars, traditionally attributed to self-absorbed synchrotron emission in conical jets.
• To investigate whether internal shocks from variable shell ejections can reproduce observed spectral energy distributions and variability.
• To explore the role of shell mass, Lorentz factor differences, ejection timing, and thermal expansion in shaping spectral and lightcurve properties.
• To identify parameter regimes that produce high, flat radio fluxes consistent with observations, overcoming the challenge of adiabatic losses reducing radio emission.
• To lay the foundation for future inclusion of synchrotron self-Compton processes and electron radiative losses.

Proposed method

• Model jet emission using discrete, time-ordered ejecta (shells) with variable bulk Lorentz factors (Γ), mass, and width.
• Simulate collisions between faster, later-ejected shells and slower, earlier ones, using inelastic collision dynamics with momentum and energy conservation.
• Calculate merged shell properties including Lorentz factor (Γₘ) and internal energy (E_in) using relativistic momentum and energy balance equations.
• Determine shock widths via hydrodynamic jump conditions, accounting for forward and reverse shocks in the lab frame.
• Compute synchrotron radiation spectra based on electron energy distributions and magnetic field energy density (u_B), assuming optically thick to thin transitions.
• Vary key parameters such as jet kinetic luminosity (L_W), ejection frequency (1 Hz), shell width, and thermal energy fraction (u_th) to explore spectral and lightcurve outcomes.

Experimental results

Research questions

• RQ1 Can internal shocks from discrete, variable-speed shell ejections reproduce the flat radio-IR spectra observed in microquasars?
• RQ2 How do variations in shell mass, Lorentz factor differences, and ejection timing affect the spectral energy distribution and lightcurve morphology?
• RQ3 Why do observed radio fluxes remain high despite significant adiabatic energy losses in shocked shells?
• RQ4 What role does shell thermal expansion (via u_th) play in determining the timescale for optical thinning at radio frequencies?
• RQ5 How do parameters like jet luminosity, Γ_max, and shell width influence the degeneracy in producing flat spectra?

Key findings

• Higher jet kinetic luminosity increases shell mass, leading to greater energy density and prolonged optical thickness at radio frequencies, which suppresses radio flux and alters spectral shape.
• With low luminosity (e.g., 1×10³³ erg s⁻¹), shells become optically thin to radio quickly, resulting in higher radio flux relative to IR, consistent with Figure 3’s spectrum.
• A flat radio-IR spectrum is difficult to achieve due to strong adiabatic losses in expanding shells, even when collisions re-energize particles.
• The ejection frequency of 1 Hz produces lightcurves and spectra resembling observed X-ray binary flares, particularly matching the break frequency in Cygnus X-1’s hard state power spectra.
• The model shows that Γ_max, L_W, and shell width have nearly degenerate effects on energy density, influencing both spectral shape and flux levels.
• Flaring in radio and IR lightcurves arises from the competition between re-energization via collisions and energy loss via adiabatic expansion.