We present an observational test of the hypothesis that leaking p modes heat the solar chromosphere. The amplitude of the leaking p modes in magneto-acoustic portals is determined using MOTH and MDI data. We simulate the propagation of these modes into the chromosphere to determine the height where the wave energy is dissipated by shock waves. A statistical approach is then used to check if this heating process could account for the observed variability of the intensity in the Lyman-α emissio

Finsterle, W.

Haberreiter, M.

Kosovichev, S.

Schmutz, W.

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Waves & Oscillations in the Solar Atmosphere:Heating and Magneto-SeismologyProceedings IAU Symposium No. 247, 2007R. Erde´lyi & C. A. Mendoza-Bricen˜o, eds.c© 2008 International Astronomical Uniondoi:10.1017/S1743921308014683P-mode leakage and Lyman-α intensityW. Finsterle1, M. Haberreiter1, S. Kosovichev2 and W. Schmutz11PMOD/WRC, Dorfstr. 33, CH-7260 Davos Dorf, Switzerland2HEPL, Standford University, Stanford CA, U.S.A.email: wolfgang@pmodwrc.chAbstract. We present an observational test of the hypothesis that leaking p modes heat thesolar chromosphere. The amplitude of the leaking p modes in magneto-acoustic portals is de-termined using MOTH and MDI data. We simulate the propagation of these modes into thechromosphere to determine the height where the wave energy is dissipated by shock waves. Astatistical approach is then used to check if this heating process could account for the observedvariability of the intensity in the Lyman-α emission.Keywords. waves, Sun: atmosphere, Sun: photosphere, Sun: chromosphere, Sun: oscillations,Sun: magnetic ﬁelds, Sun: UV radiation1. IntroductionIn magnetized areas p modes can escape the internal acoustic cavity of the Sun andpropagate upwards into the solar chromosphere (De Pontieu et al. 2003ab, Jeﬀeries et al.2006, Marsh & Walsh 2006). The underlying mechanism is thought to be wave conversionfrom sound waves into predominantely magnetic waves. A comprehensive review of theinvolved mechanisms can be found in Campos (1987) or De Pontieu & Erde´lyi (2006). Asthe pressure and density of the plasma decreases with height the pressure ﬂuctuations ofthe wave can no longer be considered inﬁnitesimal and hence the wave crest is signiﬁcantlyaccelerated due to the temperature increase induced by the wave itself. This eventuallyleads to the formation of a shock front, i.e. a quasi non-linear increase of pressure andtemperature. The shock front continues to travel upwards while dissipating its energyand thus heating the plasma. In this paper we simulate this heating process and we canshow that the induced temperature ﬂuctuations in the chromosphere qualitatively agreewith the oscillation pattern of the Lyman-α intensity observed with TRACE.2. Numerical Simulation of Leaking P ModesWe simulate the propagation of acoustic waves in a modiﬁed VAL atmosphere structurefor quiet Sun (Vernazza et al. 1981). The simulation is based on a 1-d code by Kosovichev& Popov (1981). The wave-induced temperature ﬂuctuations are shown in Figure 1, wherea 2-4 mHz frequency-ﬁltered wave train measured by MDI (Scherrer et al. 1995) in a plagepixel on January 20, 2003 was used to drive the simulation. The pixel was chosen from anarea where the concurrent observations of the MOTH instrument (Finsterle et al. 2004)reveal upward traveling waves in the p-mode frequency range (Haberreiter & Finsterle2007). Figure 1 shows that the temperature in above ∼700 km is strongly aﬀected by theshock fronts in a typical, quasi-periodic manner. Lyman-α intensity observed by TRACE(Handy et al. 1999) in plage regions shows a very similar periodicity (see Section 3), hencesuggesting that the leaking p modes modulate the solar Lyman-α emission. On average,the chromospheric temperature is hotter than if no shocks were present. However, in thewake of strong shocks occasional cooling down to ∼3500 K also occurs perdominantely74at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921308014683Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 17:09:26, subject to the Cambridge Core terms of use, availableP-mode leakage and Lyman-α intensity 75Figure 1. 1-d numerical simulation of the chromospheric temperature structure in a regionwhere p modes escape the internal acoustic cavity of the Sun. The simulation is driven by apiston at the base of the photosphere. The MDI line-of-sight velocity as measured in an areawhere the MOTH instrument detects leakage of p modes is used for driving the piston.Figure 2. The temperature vs. height for the quiet Sun model atmosphere (solid line). Thedashed line shows the temporal average of the temperature when leaking p modes form shocksin the solar chromosphere. Because p-mode leakage is closely related to magnetic ﬁelds thismechanism could explain why the chromosphere appears hotter in plage than in quiet Sunareas.at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921308014683Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 17:09:26, subject to the Cambridge Core terms of use, available76 W. Finsterle et al.0 2 4 6 8mHz0.000.050.100.150.200.250.30oscillatory amplitude [arbitrary units]Figure 3. The observed variability of Lyman-α intensity (TRACE, solid line) and the simulatedvariability of the temperature in the line-forming layer (1.5 2 Mm, dotted line). The temperaturein the line-forming layer is directly aﬀecting the intensity of the emission line. The increasedpower around 3-4 mHz is due to leaking p modes.around 1 Mm (black and dark blue areas in Figure 1). These could be the regions wheresolar molecular lines are observed (e.g. Ayres et al. 1986). The temporal average of theshock-induced heating results in a chromospheric temperature structure which resemblesthe “true” temperature stratiﬁcation in a magnetized (plage) model atmosphere (Figure2).3. Comparison with Observed Lyman-α VariabilityThe oscillatory spectrum of Lyman-α observations in a plage region by TRACE isshown in Figure 3 (solid line). The TRACE spectrum was derived from a 71-minuterun with one minute sampling interval. The dotted line is the oscillatory spectrum of thesimulated temperature between 1.5 and 2.0 Mm above the photosphere. Both curves showa prominent peak in the 3-4 mHz area, indicating that the shock-induced temperatureﬂuctuations could indeed be responsible for the observed Lyman-α variability. On largertime scales, the same mechanims could even cause the solar cycle related intensity changesin Lyman-α emission due to the changing surface fraction of magnetized areas on thesolar disk.4. Results and DiscussionP-mode induced shocks modify the temperature stratiﬁcation of a standard quiet Sunatmosphere to closely resemble that for a plage atmosphere (Figure 2). Since p modesleakage predominantely occurs in magnetic areas the described mechanism could explainwhy the chromosphere in plage appears hotter than in quiet Sun. We found that Lyman-α intensity oscillations in the p-mode frequency range are comparable to the simulatedat https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921308014683Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 11 Jul 2017 at 17:09:26, subject to the Cambridge Core terms of use, availableP-mode leakage and Lyman-α intensity 77temperature oscillations of the chromosphere when realistic assumptions for the drivingpiston are extracted from observations (Figure 3).AcknowledgementsThis work was supported by the Swiss National Science Foundation under SNF grant200020-109420.ReferencesAyres, T.R., Testerman, L., & Brault, J.W. 1986, ApJ, 304, 542Campos, L. M. B. C. 1987, Rev. Modern Phys., 59, 363De Pontieu, B., Tarbell, T., & Erde´lyi, R. 2003, ApJ, 590, 502De Pontieu, B., Erde´lyi, R., & de Wijn, A. G. 2003, ApJ, 595, L63De Pontieu, B., & Erde´lyi, R. 2006, Phil. Trans. Roy. Soc. A 364, 383Finsterle, W., Jeﬀeries, S. M., Cacciani, A., Rapex, P., Giebink, C., Knox, A., & DiMartino, V.2004, Solar Phys., 220, 317Haberreiter, M., & Finsterle, W. (2007), Solar Phys., submittedHandy, B.N., & the TRACE team 1999, Solar Phys., 187, 229Jeﬀeries, S.M., McIntosh, S.W., Armstrong, J.D., Bogdan, T.J., Cacciani, A., & Fleck, B. 2006,ApJ, 648, L151Kosovichev, A. G., & Popov, Y. P. 1981, BULLETIN. CRIMEAN ASTROPHYSICAL OBS,63, 15Marsh, M. S., & Walsh, R. W., 2006, ApJ, 643, 540Scherrer, P., & the MDI team 1995, Solar Phys., 162, 129Vernazza, J., Avrett, E., Loeser, R. 1981, ApJS, 45, 635at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921308014683Downloaded from https:/www.cambridge.org/core. 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P-mode leakage and Lyman-α intensity

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