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Paper: The Luminosity Phase Space of Galactic and Extragalactic X-Ray Transients Out to Intermediate Redshifts
Authors: Ava Polzin, Raffaella Margutti, Deanne L. Coppejans, Katie Auchettl, Kim L. Page, Georgios Vasilopoulos, Joe S. Bright, Paolo Esposito, Peter K. G. Williams, Koji Mukai, Edo Berger
Figure caption: The density of light curves in our phase space with the corresponding classes of transient underplotted; the color bar is logarithmic, and larger bins were used for the transient classes than for the overall observations. Though we only show the density of the representative data included in this paper (and so not the comprehensive density of all observations in this energy band, though this sample should span a representative range in observed X-ray luminosity and duration), certain trends are notable that are generally relevant, including that the best-sampled classes of transient are either Galactic phenomena (such as cool stellar flares or novae) or high-luminosity extragalactic transients such as GRBs and short GRBs and that there is a paucity of observations of relatively short duration events at intermediate luminosities. We use crosshatches to mark the general region of the phase space where we would anticipate, but do not yet have, observations of magnetar flares and outbursts (pink) and SBOs from stellar explosions (light blue), among other events. We note that, though it is possible that the soft X-ray emission from giant flares of magnetars may be comparable in luminosity to what has been observed in the hard X-rays (peak L X ∼ 1047 erg s−1; Hurley et al. 2005), given the paucity of soft X-ray observations of giant flares, we define the “expected” region of the DLPS for magnetar flares and outbursts based on available data.
Paper: The Luminosity Phase Space of Galactic and Extragalactic X-Ray Transients Out to Intermediate Redshifts
Authors: Ava Polzin, Raffaella Margutti, Deanne L. Coppejans, Katie Auchettl, Kim L. Page, Georgios Vasilopoulos, Joe S. Bright, Paolo Esposito, Peter K. G. Williams, Koji Mukai, Edo Berger
Figure caption: X-ray phase space of transients and variable phenomena, including GRB afterglows, SNe, SN SBOs, TDEs and AGNs, FBOTs, CVs, magnetar flares/outbursts and FRBs, cool stellar flares, XRB outbursts, and ULXs. Main panel: X-ray luminosity evolution with rest-frame time since identification. Theoretical SBO peak L X–duration points are shown with different symbols corresponding to the model’s input parameters; see Section 2.2 for details. Right side panel: to offer a sense of their persistent behavior, the quiescent/preflare luminosities of the included variable classes (AGNs, magnetar flares/outbursts, cool stellar flares, XRBs, and ULXs) are shown as horizontal bars.
Paper: The Luminosity Phase Space of Galactic and Extragalactic X-Ray Transients Out to Intermediate Redshifts
Authors: Ava Polzin, Raffaella Margutti, Deanne L. Coppejans, Katie Auchettl, Kim L. Page, Georgios Vasilopoulos, Joe S. Bright, Paolo Esposito, Peter K. G. Williams, Koji Mukai, Edo Berger
Figure caption: We compare existing observations of transients with unclear/debated classification (Table A10) with our established X-ray phase space as described in Section 3.1. These signals are colored according to their preferred classification, though in cases where no one model is considered a better match (CDF-S XT1), we give them their own “oddball” color to differentiate them from the already classified transients in the phase space. For sources with uncertain distance estimates, each estimate is shown, with the relevant distance stated in parentheses. Included events are listed in Table A10.
Paper: The Luminosity Phase Space of Galactic and Extragalactic X-Ray Transients Out to Intermediate Redshifts
Authors: Ava Polzin, Raffaella Margutti, Deanne L. Coppejans, Katie Auchettl, Kim L. Page, Georgios Vasilopoulos, Joe S. Bright, Paolo Esposito, Peter K. G. Williams, Koji Mukai, Edo Berger
Figure caption: Left panel: the peak X-ray luminosity vs. time above half-maximum light. Right panel: at left, the overall energy released during the event vs. the duration of the transient event, and at right, the distribution of isotropic equivalent energies released for each class of transient/variable. As in Figure 1, theoretical SBO peak L X–duration point markers correspond to different input parameters in the model. Points are colored according to the class of transient to which they belong; we use the same color coding as in Figure 1 and the histogram at the far right.
Paper: The Luminosity Phase Space of Galactic and Extragalactic X-Ray Transients Out to Intermediate Redshifts
Authors: Ava Polzin, Raffaella Margutti, Deanne L. Coppejans, Katie Auchettl, Kim L. Page, Georgios Vasilopoulos, Joe S. Bright, Paolo Esposito, Peter K. G. Williams, Koji Mukai, Edo Berger
Figure caption: Here we show the roughly inverse relation between instrument FOV and depth with a summary of these specifications for existing and planned/proposed X-ray missions (see Table 2 for more details). We report the 1 ks 0.3–10 keV sensitivity. Upcoming/proposed instruments are highlighted by an additional marker outline.
Paper: Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events
Authors: Shiyan Zhong, Kimitake Hayasaki, Shuo Li, Peter Berczik, Rainer Spurzem
Figure caption: Dependence of the number density of the bound stars on the orbital eccentricity. The red histogram represents the simulated number density, while the solid black and light blue lines delineate the theoretical number densities with Q boost = 1 and with Q boost = 5, respectively. Note that the theoretical number density is computed by Equation (16). The left panel corresponds to the M BH = 0.01 case, while the right panel corresponds to the M BH = 0.05 case. The error bars indicate the statistical uncertainty corresponding to the standard deviation.
Paper: Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events
Authors: Shiyan Zhong, Kimitake Hayasaki, Shuo Li, Peter Berczik, Rainer Spurzem
Figure caption: Black hole mass dependence of two characteristic eccentricities: ﹩{e}_{\min }﹩ and e lcb in the e–β plane. We adopt the Bahcall–Wolf density cusp and Q boost = 5 for all the models. The left panel shows the β-dependence of ﹩{e}_{\min }﹩ and e lcb for the M BH = 103 M ⊙ and 104 M ⊙ cases. The dashed lines denote the eccentricity, e lcb, between the empty and full loss-cone regimes (see Equation (24)), whereas the solid lines denote the eccentricity, ﹩{e}_{\min }﹩, of most tightly bound stars (see Equation (29)). The different color shows the different black hole mass. In the right panel, all the lines represent ﹩{e}_{\min }﹩. We adopt different line styles for the different black hole masses for 103 M ⊙ ≤ M BH ≤ 108 M ⊙.
Paper: Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events
Authors: Shiyan Zhong, Kimitake Hayasaki, Shuo Li, Peter Berczik, Rainer Spurzem
Figure caption: Energy dependence of the cumulative number densities for both the bound (left panel) and unbound (right panel) disrupted stars with M BH = 0.01 cases. In each panel, the red histogram shows the simulated number density (﹩{dN}/{dE}﹩), whereas the gray line represents the double-power-law curve, which is fitted to the simulated number density using an equation taking the same functional form of Equation (20), but replacing the density and radius quantities with the number density and energy, respectively.
Paper: Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events
Authors: Shiyan Zhong, Kimitake Hayasaki, Shuo Li, Peter Berczik, Rainer Spurzem
Figure caption: Black hole mass dependence of r crit/r h. The two slopes for the density profiles: s = 1.75 (Bahcall–Wolf cusp) and s = 1 (N-body simulations) are adopted.
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: (a) Single power-law electron spectrum and associated uncertainties (STEP/EPT) for the 2020 November 24 electron event in Figure 3(a). (b) Triple power-law electron spectrum (EAS/STEP/EPT) for the 2021 October 9 electron event in Figure 3(b). (c) Double power-law electron spectrum (EAS/STEP/EPT) for the 2022 April 15 electron event in Figure 3(c).
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: Top: Electron c/v versus time plot (EPD-STEP). Middle: Dynamic spectrum of the type III solar radio burst (RPW), and Langmuir wave [V 2/Hz] flux (RPW) above thermal level versus time, both associated with the event shown on the top panel. Bottom: f pe [kHz] versus time. Column (a) shows the 2020 November 24 electron event, column (b) shows the 2021 October 9 electron event, and column (c) shows the 2022 April 15 electron event. In these three cases, Solar Orbiter was at 0.901, 0.679, and 0.504 au, respectively.
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: Top panels of each column: Black dotted lines represent the STEP peak electron flux observed during each event at each energy [keV]. Colored lines represent the electron velocity distribution function at the given times. Bottom panels of each column: The associated Langmuir wave flux, with colored lines indicating the time stamps at which the electron flux slices in the top panels were taken. Column (a) shows the 2020 November 24 event, column (b) shows the 2021 October 9 event, and column (c) shows the 2022 April 15 event.
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: Top panel of each column: Pitch-angle (Θ) distribution (EPD/STEP). Bottom panel of each column: Directional and total magnetic field (MAG). Column (a) shows the 2020 November 24 electron event at 0.901 au, column (b) shows the 2021 October 9 electron event at 0.679 au, and column (c) shows the 2022 April 15 electron event at 0.504 au.
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: X-ray and EUV observations of the 2021 October 9 (left panels, (a) and (b)) and 2022 April 15 (right panels, (c) and (d)) events. Top panels ((a) and (c)): X-ray lightcurves from the GOES/XRS 1–8 Å channel (black), and the STIX 6–10 keV (red, thermal) and 20–50 keV (blue dashed, nonthermal) spectral ranges. The gray regions show the intervals over which STIX counts were integrated to produce images. Bottom panels ((b) and (d)): STIX X-ray image contours overlaid on the closest available EUV images. Panel (b) shows an AIA 171 Å image reprojected to Solar Orbiter's viewing position. Panel (d) shows an EUI Full Sun Imager 174 Å image. The STIX contour colors correspond the same spectral ranges shown in the top panels, and the contour levels correspond to 30%, 50%, 70%, and 90% of the maximum intensity in each spectral range. The STIX images were produced with the CLEAN algorithm using a CLEAN beam of 20.” The pointing uncertainty of these STIX observations is 10.”
Paper: Solar Electron Beam—Langmuir Wave Interactions and How They Modify Solar Electron Beam Spectra: Solar Orbiter Observations of a Match Made in the Heliosphere
Authors: Camille Y. Lorfing, Hamish A. S. Reid, Raúl Gómez-Herrero, Milan Maksimovic, Georgios Nicolaou, Christopher J. Owen, Javier Rodriguez-Pacheco, Daniel F. Ryan, Domenico Trotta, Daniel Verscharen
Figure caption: Position of Solar Orbiter on 2020 November 24 (a), 2021 October 9 (b), and 2022 April 15 (c). The grid in black corresponds to the Carrington coordinate system. These polar plots are generated using the Solar-MACH tool                    (Gieseler et al. 2023).
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Left: velocity field map of 12CO J = 2 → 1. Red marks the high-velocity cloud, and darker blue the low-velocity cloud. The lighter blue in the Galactic northeast of the plot is gas associated with the overlapping H II region. Note that the H II region has a different velocity from the nearby G5 gas. Right: velocity dispersion map of 12CO J = 2 → 1. The elevated dispersion in red marks the interface between the two clouds where they overlap. Note that the elevated dispersion is due to overlapping spectral features, see Figure 9. There is not a very wide spectral feature over all of the area. Black-dashed line contours denote 12CO J = 2 → 1 integrated intensity with five contours evenly spaced between the 0.25th and 99.75th percentiles.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: PV diagrams of Field 2 of G5, scaled by asinh. First row: the first image represents 13CO J = 2 → 1 and the second image C18O J = 2 → 1. Second row: HC3N J = 24 → 23, H2CO J = 321 → 220. Third row: SiO J = 5 → 4, H2CO J = 303 → 202. The PV diagram of HC3N has no detection of HC3N, but it is contaminated with emission from H2CO J = 303 → 202 (150 km s−1 to 200 km s−1), CH3OH J = 422 → 312 (−50 km s−1 to 0 km s−1), and H2CO J = 322 → 221 (−100 km s−1 to −50 km s−1). The PV diagram of H2CO H2CO J = 321 → 220 is contaminated with emission from OCS J = 18 → 17 at velocities between −100 and −50 km s−1.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: PV diagram of Field 2 in 12CO J = 2 → 1, averaged over Galactic latitude and taken horizontally across the field with a width of 2′. Features are labeled in Figure 18 in the Appendix.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Dust emissivity SED fit of G5's Field 2 with a modified blackbody using dust_emissivity. We used Herschel SPIRE and PACS data from the Hi-GAL survey (Molinari et al. 2016) for wavelengths 70, 160, 250, 350 and 500 μm. We used ATLASGAL for 850 μm (Schuller et al. 2009) and BGPS for 1.1 mm (Ginsburg et al. 2013). The error bars are the quadrature sum of statistical uncertainty (background noise) and inherent uncertainty due to flux calibration. The fit for the modified blackbody resulted in a dust temperature of 18.09 K ± 1.19 K, β of 1.75  ± 0.29 , and column density of 4.34 × 1021 cm−2 ± 0.68 × 1021 cm−2.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Histogram of the calculated 12CO opacity of Field 2 assuming 12C/13C = 40. Green shows the opacity values for voxels in the velocity bridge. Orange represents opacity values for the higher-velocity cloud, G5a. Blue shows the opacity values for the lower-velocity cloud G5b. Red represents the opacity values for the line-of-sight clouds between velocities of −50  to ∼15 km s−1.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Ratios of integrated-intensity maps were taken of Field 2 and then averaged over the Galactic latitude to show how the values change horizontally across the field in Galactic longitude. Black shows the ratios measured by taking the ratio of the integrated intensities over all of the cubes. The gray error bars show the standard deviation over the averaged area. Orange shows the ratios when the integrated intensities were limited to velocities associated with G5a, the higher-velocity cloud. Blue shows the ratios when the integrated intensities were limited to velocities associated with G5b, the lower-velocity cloud.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Plot of the simulated integrated intensities of SiO J = 5 → 4 (top) and H2CO J = 303 → 202 (bottom) for different volume densities and abundances at a gas temperature of 60 K. Th orange span covers the measured integrated intensities for the higher-velocity cloud G5a, and the blue span covers the same for the lower-velocity cloud G5b. The upper limits of the colored spans are the maximum detected integrated intensities, and the lower limits are the detection threshold.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Two integrated-intensity maps of G5 in 12CO J = 2 → 1 to show the distinct velocity components. Top: integrated intensity map of G5a, from velocities 75–200 km s−1. Bottom: integrated-intensity map of G5b, from velocities of 15–75 km s−1. This map was taken starting from 15 km s−1 to avoid emission from line-of-sight clouds in the Milky Way’s spiral arms.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Histogram of the gas temperatures of G5a, the high-velocity cloud in orange, and G5b, the low-velocity cloud in blue. The average temperatures of the two clouds are 63 K ± 19 K for G5a and 60 K ± 14 K for G5b. This figure shows how much of each cloud is in each temperature bin, separated between G5a and G5b. A K-S test between the two clouds resulted in a p-value ≪1, meaning that the temperatures of G5a and G5b do not come from the same distribution.
Paper: Scale Invariance in Gamma-Ray Flares of the Sun and 3C 454.3
Authors: Fang-Kun Peng, Jun-Jie Wei, Hai-Qin Wang
Figure caption: The best-fitting q values from Equation (1) with 1σ regions (shaded) as a function of n for gamma-ray flares of the Sun (left panel) and 3C 454.3 (right panel), respectively. The uncertainties of q values for waiting time are not shown for clarity.
Paper: Scale Invariance in Gamma-Ray Flares of the Sun and 3C 454.3
Authors: Fang-Kun Peng, Jun-Jie Wei, Hai-Qin Wang
Figure caption: The relationship between parameters q (from the q-Gaussian function) and α (from the size frequency distribution) for gamma-ray flares of the Sun (left panel) and 3C 454.3 (right panel), respectively. The dashed line shows the predicted curves from Equation (4). Data points with 2σ error bars correspond to the best-fitting values of q and α estimated for the energies (blue dot), peak luminosities (red dot), duration times (green dot), and waiting times (black dot), respectively.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Cartoon of a top-down view of the Milky Way’s bar. Not to scale. Two bar lanes bring material falling from X1 orbits to X2 orbits. The yellow burst markers are some of the sites where cloud–cloud collisions are thought to happen between streams of gas. G5 is the likely site of a collision between overshooting gas from the farside bar lane and the nearside bar lane. G1.3 is the likely site of gas accreting onto the CMZ from the nearside bar lane (Busch et al. 2022). The dashed lines represent lines of sight from positions in the center of the Galaxy and along the bar to the observer’s position. The gray ellipse represents X1 orbits. The yellow circle represents X2 orbits, which could be the CMZ.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: The process of percentile subtraction along the spectral axis, as detailed in Section 3.3. (Left) PV diagram of H2CO 321 → 220 using a raw data cube. Note the spectral ripple. (Middle) Fifth percentile spectrum of the raw data. Note that the troughs in the percentile spectrum line up in velocity space with the baseline ripple in the Left panel. (Right) PV diagram of H2CO 321 → 220 after subtracting the 5th percentile spectrum. The baseline ripple has been removed with the baseline centered on 0 K.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Three-color image of Herschel SPIRE 250 μm, PACS 70 μm, and MIPSGAL 24 μm overlaid with NH3 (3,3) integrated-intensity contours [6.8, 11.0, 17.8] from the Mopra HOPS Survey (Walsh et al. 2011; Purcell et al. 2012; Longmore et al. 2017).
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: Wider context images of G5 showing the projected environment around the cloud using Herschel and Spitzer data. The H II region in the field is not associated with G5. The white contours are from the integrated-intensity map of H2CO (303–202), and do not seem to follow the morphology of the images. Left: three color Spitzer image of MIPSGAL 24, 8.0, and 4.5 μm. Right: three color image of Herschel SPIRE 250 μm and PACS 70 μm, and MIPSGAL 24 μm.
Paper: Evidence of a Cloud–Cloud Collision from Overshooting Gas in the Galactic Center
Authors: Savannah R. Gramze, Adam Ginsburg, David S. Meier, Juergen Ott, Yancy Shirley, Mattia C. Sormani, Brian E. Svoboda
Figure caption: PV diagram of Field 2 in 12CO J = 2 → 1, averaged over Galactic latitude and taken horizontally across the field with a width of 2′. This is the same as Figure 8, but with the features detailed in Section 4.2 labeled.
Paper: Scale Invariance in Gamma-Ray Flares of the Sun and 3C 454.3
Authors: Fang-Kun Peng, Jun-Jie Wei, Hai-Qin Wang
Figure caption: Scale-invariance structure of solar GeV flares. Cumulative distributions with q-Gaussian function (solid lines) for the differences of fluences (upper left panel), peak fluxes (upper right panel), duration times (lower left panel), and waiting times (lower right panel) for n = 1 (circles), n = 8 (crosses), and n = 15 (stars), respectively.