Temporal Variations of the VHE γ-Ray Emission

Comparison with IC Model

Figure 6.8 shows the comparison of the VHEγ-ray light curve and the IC model by Kirk et al.

[1999] for dominant adiabatic and radiative (IC) losses for B = 0.32 G. The light curve was recalculated using a 2-day flux average in order to reduce the statistical error on each flux point at the expense loosing details. It is clear, that both model curves disagree with the measurement, in particular the indication for a flux minimum near periastron and a peak at≈ τ+25 days. Nev-ertheless, the disagreement is not surprising since the variability pattern indicates an enhanced VHEγ-ray flux during the epochs of the interaction of the pulsar wind and the stellar disk which was neglected in the model.

−20 τ 20 40 60 τ

80 100

−1−2−12EF (1TeV) [10 TeV cm s ]

Time [days relative to periastron ]

0

E

2 4

Time [MJD]

53060 53080 53100 53120 53140 53160 53180

6

Kirk et al. 1999, dominant adiabatic losses Kirk et al. 1999, dominant radiative losses H.E.S.S. data 2004, 2−day average

Inverse Compton Scenario

pulsar radio eclipse

Figure 6.8: Model light curves of the VHE γ-ray energy flux according to Kirk et al. [1999] for dominant adiabatic and radiative losses (dashed and dotted line, respectively). The full points represent the flux measured by H.E.S.S. averaged over a time period of two days for each point.

Inverse Compton Drag Near Periastron

The indication of a low flux level at the periastron passage suggests that the shock-accelerated electrons are less efficiently produced or loose their energy much faster than during the phases of high flux before and after periastron.

Firstly, the high density of thermal photons from SS 2883 near periastron might decelerate the pulsar wind before it is terminated by the stellar mass outflow and much less electrons with the nominal Lorentz factor are available for shock acceleration. This scenario of theγ-ray emission from the unshocked wind was excluded from the measured spectrum in the range of wind Lorentz factors between γ_wind ≈ 10⁶. . .10⁸ to be responsible for the observed VHE γ-rays. However, since the energy threshold for the observations of PSR B1259−63 is higher than 300 GeV, the emission from the unshocked wind with Lorentz factors below the threshold and above the maximum energy of≈ 10 TeV the analysis was sensitive to would remain undetected by the H.E.S.S. observations.

Thus, the unshocked wind scenario might account for the observed flux decrease of VHE γ-rays and non-thermal X-γ-rays a few days around periastron. However, the observed asymmetry of the γ-ray flux with respect to periastron cannot be explained by the inverse Compton drag alone.

Interaction of the Pulsar Wind with the Stellar Disk Outflow

The indication of two flux maxima, several days pre- and post-periastron suggest a connection between the high flux states and the crossings of the pulsar through the regions of enhanced mass outflow in the stellar disk of SS 2883.

The fact that both the X-ray and VHEγ-ray fluxes have a minimum during periastron ex-cludes that radiative losses via synchrotron or IC emission of the accelerated electrons domi-nate. On the other hand, if adiabatic energy losses of the shock-accelerated electrons dominate, as suggested by the spectral shape of theγ-ray emission, the variability pattern can be explained with a varying confinement of the pulsar wind by the stellar outflow [Aharonian and Völk, 2004]

illustrated in Fig. 6.9.

stellar

Figure 6.9: Schematic geometry of the interac-tion between the pulsar and stellar winds near periastron. The down-stream shock regions are compressed during the phase of pulsar wind – disk interaction while at periastron, these regions are less compact allowing a more rapid expan-sion of the plasma.

During the interaction of the pulsar wind with the disk, the down-stream regions of the shocks are relatively compact and close to the pulsar with a relatively slow post-shock plasma flow along the contact discontinuity away from SS 2883. In the regions where the pulsar wind interacts with the less dense polar component of the stellar outflow, the shock occurs less close to PSR B1259−63 and the heated plasma can rapidly expand in the down-stream region. This scenario can qual-itatively explain the two high flux states at the pulsar disk crossings and a flux minimum near periastron for all radiation components produced in the down-stream regions of both wind termination shocks.

Stellar Disk Orientation

The general connection of the radiation flux level with the stellar wind density is sup-ported by the correlation between the γ-ray light curve and that of the X-ray and unpulsed radio emission near periastron.

The variability pattern of the X-ray emis-sion near periastron also showed two flux maxima near periastron with a minimum at periastron which was modeled by Tavani and Arons [1997] to be compatible with an

in-clined disk withω_disk ≈120^◦. The calculated timescales of the shock-acceleration and dominant energy loss processes of the order of hundreds of seconds (c.f. Fig. 2.17) require the peak emis-sion to occur at the time of the disk crossing. Since the VHE γ-ray production is assumed to originate from the same electron population as the X-ray emission, the VHEγ-ray flux maxima can be interpreted to correspond as well to the times of the disk crossings. Using the post-periastron maximum of theγ-ray flux at aroundτ+25±5 days as a reference time for the disk crossing, the corresponding disk orientation would beω_disk≈ 105^◦as it is illustrated in Fig. 6.10 with the dashed line. The expected peak of the pre-periastron disk crossing would lie in this case atτ−12 days which is compatible with the VHEγ-ray light curve.

In contrast, the peaks of the unpulsed radio emission (see Fig. 6.3) were interpreted by Ball et al. [1999] in the case of an inclined disk as synchrotron radiation from electrons shock-accelerated on the Be star side shock of the pulsar wind “bubble” (c.f. Sec. 2.3.3). In this model, the bubble decays slowly by synchrotron losses only and thus shows a peak flux a few days after the assumed disk crossings of the pulsar for a disk orientation withωdisk ≈90^◦. Since the VHE γ-ray emission shows a correlated flux enhancement one could assume the same mechanism to be responsible for the γ-ray emission. This would be contrary to the case above, where

dynamical flow effects on timescales of minutes were considered to be important, and the peak emission would directly correspond to the phases of the crossings.

ωd

Figure 6.10: Orbit of PSR B1259−63 near periastron (c.f. Fig. 2.8). The solid, dashed and dotted straight line illustrate different ori-entations of the stellar disk.

Alternatively, the electrons responsible for the radio emission could be accelerated in the Be star side shock as required by Ball et al. [1999]

but could evolve similarly to the pulsar wind shock electrons, i.e. rapidly loosing their energy by dominant adiabatic expansion instead of slow synchrotron cooling, and thus the observed radi-ation would be correlated at all photon energies.

Flux Level Differences Between the Disk Crossings

In the case, where the γ-ray flux peaks corre-spond to the times of the pulsar disk passages, the question remains why the flux near the post-periastron passage seems enhanced with respect to the first passage, although the peak flux pre-periastron was not covered by the H.E.S.S. ob-servations.

Firstly, if the disk crossings are not symmetrical with respect to periastron, i.e.ω_disk > 90^◦, the pulsar wind would be terminated closer to the pulsar during the first crossing and thus the magnetic field strength in the plasma would be higher (c.f. Fig. 2.17), resulting in a suppression of theγ-ray flux by enhanced synchrotron losses compared to the second crossing, while the X-ray flux level would show the opposite behaviour (c.f. Fig. 2.16). Secondly, theγ-rays produced during the first crossing have to travel through a region with a higher density of thermal photons from SS 2883 compared to the second crossing and thus may be more strongly absorbed bye^± pair production [Kirk et al., 1999]. Finally, since the down-stream flow of accelerated particles proceeds along the contact discontinuity between the pulsar and stellar wind shocks along the

“comet tail” mainly in the direction away from the pulsar and its companion, one could expect a modulation of the γ-ray light curve by the Doppler shift with respect to the line of sight [de Jager, 2004]. Theγ-ray fluxF at a given pulsar orbital phase then depends on the angleθp ≡θ between the line of sight and the line pulsar/Be-star and is suppressed by a factor of

F

F₀ = 1+βcosθ 1+βcosθ₀

!Γ^γ+1

compared to a point of the orbit where this angle is minimal,θ=θ₀ ≈55^◦with a corresponding fluxF0. The key parameter is the flow velocity of the plasmaβwhich might be even supersonic withβ >c/√

3. UsingΓγ = 2.7, the angleθand the resulting flux ratio for different values ofβ are shown in Fig. 6.11 bottom and top, respectively, as a function of time for the epochs of the H.E.S.S. observations.

The Doppler shift could account for a reduction of the flux at the first compared to the second disk crossing. Note however, that the suppression due to the Doppler effect will only be applicable as long as a cometary tail exists: If the ram pressure due to the stellar wind is

Time [days relative to periastron]

τ 20 40 60 80 100

[deg]pθ0F/F Periastron

Doppler Ratio 0.2

0.4 0.6 0.8 1

=0.8

=0.4

=0.2

β β β

Time [MJD]

53060 53080 53100 53120 53140 53160

Angle Earth−Star/Pulsar

40 60 80 100 120 140

Figure 6.11: Top: Relative γ-ray flux suppression due to Doppler shifting (see text) for different down-stream plasma flow velocitiesβas a function of time for the time range of H.E.S.S. observations of PSR B1259−63. Bottom: Angle between the line of sight and the line between the pulsar and its companionθ_pas a function of time.

unable to produce a well collimated cometary tail outside the two epochs of the disk crossing no Doppler suppression is expected. Interestingly, in the case of a disk orientation symmetric with respect to periastron (with ω_disk = 90^◦) the suppression of the TeV flux could explain a delayed flux maximum which occurs several days after the second disk crossing associated with a minimal θ as stated above. Long after the periastron passage, the ram pressure in the stellar wind will again be too small to support a cometary tail, resulting in an interpretation in terms of a weakly collimated cometary tail, where Doppler effects would be less pronounced.