Constraining the Location of <i>γ</i>-Ray Flares in the Flat Spectrum Radio Quasar B2 1633+382 at GeV Energies

In this study, we extract a 7-day binned <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-ray light curve from 2008 August to 2019 March in the energy range 0.1–300 GeV and identify four outburst periods with peak flux of >8.0<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mo>×</mo><mspace width="3.33333pt"></mspace><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></semantics></math></inline-formula> ph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>cm</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup><mtext> </mtext><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. Four active states in the optical are also marked during this period. The fastest variability timescale suggests the emission region radius is <i>R</i> ∼ 2.4<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mo>×</mo><mspace width="3.33333pt"></mspace><msup><mn>10</mn><mn>16</mn></msup></mrow></semantics></math></inline-formula> cm, and the observed emission region lies within <0.7 pc distance from the central engine. The majority of short-timescale flares exhibit a symmetric temporal profile, implying that the rise and decay timescales are dominated by disturbances caused by dense plasma blobs passing through the standing shock front in the jet region. To understand the properties of the source jets, we employ a standard one-zone leptonic scenario to model the broadband spectral energy distributions (SEDs) of flaring periods and determine that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-ray spectrum is better reproduced when the dissipation region of the jet is located within the molecular torus (MT). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-ray spectra from the outburst phases show an obvious spectral break with a break energy between 3.00 and 7.08 GeV, which may be attributed to an intrinsic break in the energy distribution of radiating particles. The studies of the survival time of a sheet before being destroyed by the turbulent motions of plasma (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>∼</mo><mn>2.9</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></mrow></semantics></math></inline-formula> s), the shock acceleration time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mi>a</mi><mi>c</mi><mi>c</mi></mrow></msub><mo>∼</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.3</mn><mo>×</mo><mspace width="3.33333pt"></mspace><msup><mn>10</mn><mn>4</mn></msup></mrow></semantics></math></inline-formula> s), and the minimum interaction height (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></semantics></math></inline-formula> ≈ 2.57–4.55<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mo>×</mo><mspace width="3.33333pt"></mspace><msup><mn>10</mn><mn>17</mn></msup></mrow></semantics></math></inline-formula> cm > <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mrow><mi>B</mi><mi>L</mi><mi>R</mi></mrow></msub></semantics></math></inline-formula> ∼ 1.0<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mo>×</mo><mspace width="3.33333pt"></mspace><msup><mn>10</mn><mn>17</mn></msup></mrow></semantics></math></inline-formula> cm) suggest that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-ray flaring event maybe caused by a magnetic reconnection mechanism, but we cannot completely rule out the shock-in-jet model.