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<jats:title>Abstract</jats:title> <jats:p>The heliospheric energetic neutral atom spectrum observed by the Interstellar Boundary Explorer (IBEX) reveals that the heliosheath proton distribution is consistent with a power law. The origin of the spectrum is likely from interstellar pickup ions (PUIs) accelerated at the heliospheric termination shock (HTS). We present an explanation of the proton spectrum origin using a test particle simulation of PUIs accelerated at the HTS. PUIs experience preferential heating by the motional electric field in the shock foot, but do not develop a power-law tail without the presence of turbulence at wavenumbers (<jats:italic>k</jats:italic>) close to the PUI gyroradius scale (<jats:italic>R</jats:italic> <jats:sub>g</jats:sub>). Voyager 2 observations of the magnetic field downstream of the HTS indicate a moderate amount of turbulence at <jats:italic>kR</jats:italic> <jats:sub> <jats:italic>g</jats:italic> </jats:sub> ≅ 1, <jats:inline-formula> <jats:tex-math> <?CDATA ${\left(\delta B/{B}_{0}\right)}^{2}\cong 0.01$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>≅</mml:mo> <mml:mn>0.01</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac12ccieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, which we find to be sufficient for producing a downstream suprathermal PUI tail but not at intensities observed by IBEX. Within the shock ramp, however, Voyager observed the turbulence power at much smaller scales to be nearly 100 times stronger, suggesting the possibility of strong turbulence at the PUI gyroradius scale. We show that a proton distribution can develop a power law downstream of the HTS consistent with IBEX observations if <jats:inline-formula> <jats:tex-math> <?CDATA ${\left(\delta B/{B}_{0}\right)}^{2}\gtrsim 0.1$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>≳</mml:mo> <mml:mn>0.1</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac12ccieqn2.gif" xlink:type="simple" /> </jats:inline-formula> at <jats:italic>kR</jats:italic> <jats:sub> <jats:italic>g</jats:italic> </jats:sub> ≅ 1 in the shock foot. Shock drift acceleration of PUIs by the motional electric field is aided by interactions with turbulence upstream of the shock overshoot. Steepening of the IBEX proton spectrum in directions farther from the heliospheric nose suggests the HTS compression ratio and/or turbulence power weakens near the heliotail.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The amplitude of the 11 yr solar cycle is well known to be subject to long-term modulation, including sustained periods of very low activity known as Grand Minima. Stable long-period cycles found in proxies of solar activity have given new momentum to the debate about a possible influence of the tiny planetary tidal forcing. Here, we study the solar cycle by means of a simple zero-dimensional dynamo model, which includes a delay caused by meridional circulation as well as a quenching of the <jats:italic>α</jats:italic>-effect at toroidal magnetic fields exceeding an upper threshold. Fitting this model to the sunspot record, we find a set of parameters close to the bifurcation point at which two stable oscillatory modes emerge. One mode is a limit cycle resembling normal solar activity including a characteristic kink in the decaying limb of the cycle. The other mode is a weak sub-threshold cycle that could be interpreted as Grand Minimum activity. Adding noise to the model, we show that it exhibits Stochastic Resonance, which means that a weak external modulation can toss the dynamo back and forth between these two modes, whereby the periodicities of the modulation get strongly amplified.</jats:p>