A Model for Emission from Microquasar Jets: Consequences of a Single Acceleration Episode

1. A Model for Emission from Microquasar Jets: Consequences of a Single Acceleration Episode Asaf Pe’er (CfA / ITC) and Piergiorgio Casella (Southampton) Abstract We present a new model of emission from jets in Microquasars, which implements elements from the study of jets in gamma-ray bursts to these objects. By assuming that electrons are accelerated once at the base of the jet to a power law distribution above a low energy Maxwellian, and are cooled by synchrotron emission and possible adiabatic energy losses along the jet, a wealth of spectra can be obtained. We show our theoretical results which can explain some of the key observations. In particular, we find: (I) a flat radio spectrum, as is frequently seen, is a natural outcome of the model; (II) Strong magnetic field results in a flux decay in the optical/UV band as Fν ~ ν-1/2, irrespective of many of the uncertainties of the model. (III) An increase of the magnetic field above a critical value of ~ 105 G leads to a sharp decrease in the flux at the radio band, while the flux at higher frequencies saturates to a constant value. We conclude that scatter in the values of the magnetic field may provide a natural explanation to the observed scatter in the radio/X ray luminosity correlation seen in these objects. Background: jets in the Low/Hard state in Microquasars Spectrum- I: Maxwellian, weak magnetic field Most simplified scenario: Maxwellian distribution of energetic electrons (i.e., gmin = gmax). For B<Bcr,1 radiative cooling is not effective. From every jet segment, the resulting spectrum has 2 breaks:npeak – corresponds to sync. emission from elecs. at the peak of the distribution (gmin). nbreak- corresponds to synchrotron break (optically thick/thin transition).Result: For conical jet (a=1), flat radio spectra is obtained, because npeak decreases. The spectrum is similar to BK79, but have different physical origin ! (1) In nearby objects, elongated emission is seen. (2) Flat radio spectrum is attributed to synchrotron emission from partially self-absorbed jet (Blandford & Konigl, 1979).Basic model assumptions: (I) Electrons are power law distributed. (II) Conical jet, constant outflow velocity -> density decrease n(r) ~ r-2. (II) Poynting flux conservation -> B-field decays along the jet, B(r) ~ r-1. Synchrotron emission theory: the spectrum from a jet segment is a broken power law. The spectrum is optically thick (self absorbed) at low energies, and optically thin at high energies. Under the conditions above, the break energy decreases along the jet, while the radio flux is constant, resulting in flat radio spectrum. Cyg X-1 (Stirling+, 2001) Scale: marc-sec -> 10’s A.U Spectrum- II: Maxwellian,Intermediate B field:Fn ~ n-1/2 in optic/X Motivation: the need for a new model • State of the art models of particle acceleration (e.g., Spitkovski (2009)) predict that most of the electrons have a Maxwellian distribution with a typical Lorentz factor, gmin.; A power law distribution exists only at higher energies, between gmin and gmax. • As the electrons radiate photons, they inherently cool. This cooling affects the emitted spectrum; Thus, any emission model must take cooling into account. For B>Bcr,1 radiative cooling is important. Most of the cooling occurs close to the jet base, where the B-field is constant. The resulting spectrum in the optic/X band is Fn ~ n-1/2. 1) This result follows directly from sync. theory; It is independent on the electrons distribution (no power law here !!)or the jet geometry, since it results fromemission at the jet base. 2) Emission from larger radii – results in flat radio spectra, as above (for a=1). Basic model assumptions • Electrons are assumed to be accelerated once at the base of the jet,to a power law between gmin and gmax. • The jet geometry is a free parameter: r(x)~xa. • Pointing flux conservation: B(r)~r-1 • Inside the jet, the electrons propagate at constant velocity, they radiate and cool.Cooling is due to synchrotron emission and (possible) adiabatic energy losses. Spectrum- III: Strong B field -> suppression of radio Key result #1: Electrons cooling along the jet For stronger magnetic field, B>Bcr,2 ~ 105 G,cooling at the jet base is so rapid,that close to the jet base, npeak < nbreak;most of the emission is self absorbed. Result: Radio emission is strongly suppressed.The emission at the high energies (optic/X) is not affected. Electrons energy distribution along the jet can be phrased in a simple equation:full solution: (solid curves) only synch.: (dashed curves)(see also Kaiser, 2006)Conclusions:Along the jet, the electrons energy is characterized by:(1) Initial rapid cooling -> close to the jet base. In this regime, the B-field is nearly constant. The higher the initial B-field, the lower the electrons final energy.Physically: the electrons radiate most of their energy as synchrotron.(2) Asymptotic expansion: at larger radii, for wide jets (a>1/2), electrons maintain their energy or lose it adiabatically. Physically: since the B-field decays rapidly, radiative losses are small.(3) Narrow jets (a<1/2): electrons continuously lose their energy along the jet. Physically: the magnetic field does not decay rapidly enough. Can define “critical value” for the B-field:for B<Bcr,1~104G, the electrons radiative cooling is not effective (blue line) Comparison with observations: natural explanation to outliers Many microquasars show universal radio/X correlation (the “fundamental plane”). However, there are outliers, all show suppressed radio emission. Within the framework of our theory, Strong B-field may provide natural explanation! Radio/X flux (Soleri+, 2010) Summary • Flat radio spectrum is obtained, without the need for electrons re-acceleration ! • Intermediate B -> Fn ~ n-1/2 in the optic/X band; No elec. power law is needed ! • For strong B, radio emission is suppressed (but not emission at the X band !) • -> May provide natural explanation to the outliers seen. For further details, see: Pe’er & Casella, 2009, ApJ, 699, 1919; Casella & Pe’er, 2009, ApJ, 703, L63; or contact me at apeer@cfa.harvard.edu