THE NON-MAGNETIC SOLAR CHROMOSPHERE MATS CARLSSON Institute of Theoretical Astrophysics, P.O.Box 1029 Blindern, N{0315 Oslo, Norway and ROBERT F. STEIN Department of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA Abstract. We summarize recent results from self-consistent non-lte radiation hydrodynamics simulations of the propagation of acoustic waves through the non-magnetic solar chromosphere. References to more detailed write-ups of the work are given. The simulations closely match the observed behaviour of Ca II H 2 V bright grains. Observations of CO-lines, that are problematic to explain in semi-empirical one-component models, are consistent with the simulations. Recent observations of UV continua with the SOHO satellite are also well explained. The simulations show that for regions of the chromosphere whose structure is not obviously controlled by magnetic elds, a dynamic and not static picture is needed to describe the structure and the emitted spectrum. The whole foundation for using spectral features in static models to infer physical properties of the chromosphere must be called into question. It is found that enhanced chromospheric emission, which corresponds to an outwardly increasing semi-empirical temperature structure, can be produced by wave motions without any increase in the mean gas temperature. Thus, despite long held beliefs, the sun may not have a classical chromosphere in magnetic eld free internetwork regions at heights below 1 Mm. Lines formed above 1 Mm height show emission all the time in observations from the SOHO satellite in contrast with what is expected from the simulations. Thus, something important is missing from the calculations { perhaps concerning the fate of shock waves propagating upwards into a magnetic \canopy", perhaps concerning dierent propagation modes (MHD eects), or energetically non-connected material lying along the line of site (like magnetic ux-tubes). Key words: Hydrodynamics, Radiative transfer, Shock Waves, Sun: chromosphere 1. Introduction The resonance lines from singly ionized calcium are the best spectral diagnostics available from the ground to probe the conditions in the solar chromosphere and consequently there is a vast amount of observational material (see the review by Rutten and Uitenbroek, 1991 and references therein; Harvey et al., 1992; Lites et al., 1993; Bocchialini et al., 1994; Von Uexkuell and Kneer, 1995; Hofmann et al., 1996; Steens et al., 1996). The observations show a very dynamic behaviour with asymmetric emission in the line core and evidence for propagating acoustic waves in the intensity phase behaviour in the line wings. To study the formation of the calcium lines and the propagation of acoustic waves in the non-linear regime is non-trivial because the hydrodynamics and the
2 MATS CARLSSON AND ROBERT F. STEIN radiation couple in the formation layers and the excitation balance is far from local thermodynamic equilibrium (LTE). We therefore have to solve a very non-linear, non-local problem. We have developed a code that is capable of the necessary self-consistent radiationhydrodynamic treatment under solar chromospheric conditions with the important radiative transitions treated in non-lte. Earlier schematic studies using sinusoidal monochromatic driving velocity elds (Carlsson and Stein, 1992) have been expanded to driving velocity elds that reproduce observed Doppler shifts in photospheric lines. These simulations are used to show that the whole concept of a semistatic non-magnetic chromosphere is completely misleading. The results of the simulations have been described in detail elsewhere and we will therefore only summarize the results here. More details on continuum formation and the mean atmospheric structure can be found in Carlsson & Stein (1994, 1995); more details on the formation of Ca II grains in Carlsson & Stein (1997). 2. Method A schematic representation of the computational scheme is shown in Fig. 1. We solve the one-dimensional equations of mass, momentum, energy and charge conservation together with the non-lte radiative transfer and population rate equations, implicitly on an adaptive mesh. We employ 6 level model atoms for hydrogen and singly ionized calcium. We include in detail all transitions between these levels. Other continua are treated as background continua in LTE, using the Uppsala atmospheres program (Gustafsson 1973). Microturbulence broadening was set to a constant 2 km/s throughout the atmosphere. Our initial atmosphere is in radiative equilibrium above the convection zone (for the processes we consider) without line blanketing and extends 100 km into the convection zone, with a time constant divergence of the convective energy ux on a column mass scale. Waves are driven through the atmosphere by a piston located at the bottom of the computational domain (100 km below 500 = 1). The piston velocity is chosen to reproduce a 3750 second sequence of Doppler shift observations in an Fe I line at 396.68 nm in the wing of the Ca H-line (Lites et al. 1993). The velocity spectrum as a function of frequency changes with height, both in amplitude and phase. The velocity amplitude of propagating waves increases with height in a stratied atmosphere to maintain a constant ux as the density decreases. Damping reduces this amplitude increase. Propagating modes also show a phase shift due to their nite phase speed. Evanescent modes are attenuated but have no change in phase as a function of height. We calculate this change in amplitude and phase between the piston height and 260 km as a function of wave frequency and multiply the observed Doppler-shifts with the inverse of this transfer function to obtain our piston velocities. Comparing the simulated velocities at 260 km with the observed Doppler shift in the iron line provides a check of this procedure (Fig.1). We applied this procedure to the observed Doppler shifts at ve dierent slit positions. At the top of the computational domain there is a transmitting boundary condition.
THE NON-MAGNETIC SOLAR CHROMOSPHERE 3 Fig. 1. A schematic representation of the computational method. Observed Doppler shifts in an iron line are transformed in amplitude and phase to get a piston velocity that gives a simulated velocity at the iron line formation height (260km) close to the observed Doppler shifts. The equations of conservation of mass, momentum, energy and charge are solved together with the non-lte rate equations for 6 levels of hydrogen and 6 levels of ionized calcium implicitly on an adaptive mesh.
4 MATS CARLSSON AND ROBERT F. STEIN In the dynamic calculation only hydrogen and calcium are treated self-consistently in non-lte. With the time-variation of hydrodynamic variables (density, temperature, electron density, velocity) taken from this calculation, the statistical equilibrium equations were solved for an additional set of \minority species" (solution assumed not to inuence the hydrodynamics or energetics of the atmosphere): neutral aluminium, magnesium, silicon and carbon. 3. Results 3.1. Continuum formation The VAL3C model of the solar chromosphere uses average intensities in UV continua to constrain the mean temperature structure. The dynamic simulation shows clearly how misleading this procedure is. In UV, the Planck function has an exponential sensitivity to temperature and the average intensity therefore samples preferentially the high temperatures. This is clearly shown in Fig. 2 with the radiation temperature of the intensity mean being close to the maximum intensity and likewise for the Planck function. The source function varies much less than the Planck function due to the non-lte decoupling. The radiation temperature of the outgoing intensity does not show the shock signature of a discontinuous rise for the same reason. For more details, see Carlsson & Stein (1994, 1995). 3.2. Mean atmospheric structure The non-linear temperature response of the Planck function in UV causes the mean intensity to be much larger than the intensity corresponding to the mean temperature. If a semi-empirical model is based on mean intensities in UV (like the VAL3C model) one therefore gets temperatures above the mean temperature of the dynamic model. The time averaged temperature in the dynamic simulation actually shows no chromospheric rise (Fig. 3) while the semi-empirical temperature structure that gives the same mean intensities has a classical chromosphere. The dynamic simulation comes close in reproducing the observed mean intensities in UV continua, CO line intensities and also the dynamic behaviour in the calcium resonance lines without a chromospheric rise in the mean temperature. This picture of the non-magnetic solar chromosphere is drastically dierent from the one inferred from semi-empirical models. The mean temperature in the dynamic simulation is close to the radiative equilibrium starting model. It is important to note, however, that the mean radiation is very dierent from radiative equilibrium with enhanced emission in UV continua and strong lines. On the average there is strong radiative cooling balanced by viscous heating from shocks and from P dv -work. For more details, see Carlsson & Stein (1994, 1995). 3.3. Ca II H 2V grains The simulations closely match the observed behaviour of Ca II H 2V bright grains down to the appearance of individual grains (Fig. 4). The bright grains are produced by shocks near 1 Mm above 500 = 1. Shocks in the mid chromosphere produce a large source function (and therefore high emissivity)
THE NON-MAGNETIC SOLAR CHROMOSPHERE 5 Fig. 2. The radiation temperature of the outgoing intensity (solid), the source function at =1 (dotted) and the temperature at = 1 (dashed) as functions of time for a small part of the dynamical simulation for four wavelengths. The horizontal lines show the radiation temperature of the mean of the outgoing intensity (solid) and of the mean of the Planck function (dashed) with the mean taken over this part of the simulation. The means from the complete simulation will be slightly dierent. because the density is high enough for collisions to couple the CaII populations to the local conditions. The asymmetry of the line prole is due to velocity gradients near 1 Mm. Material motion Doppler shifts the frequency where atoms emit and
6 MATS CARLSSON AND ROBERT F. STEIN Fig. 3. Time average of the temperature in the dynamical simulation (thick solid), the range of temperatures in the simulation (thin solid), the semi-empirical model that gives the best t to the time average of the intensity as a function of wavelength calculated from the dynamical simulation (thick dashed), the starting model for the dynamical simulation (dotted) and the semi-empirical model FALA (dot-dashed). The maximum temperatures are only reached in narrow shock spikes of short duration. The semi-empirical model giving the same intensities as the dynamical simulation shows a chromospheric temperature rise while the mean temperature in the simulation does not. absorb photons, so the maximum opacity is located at { and the absorption prole is symmetric about { the local uid velocity, which is shifted to the blue behind shocks. The optical depth depends on the velocity structure higher up. Shocks propagate generally into downowing material, so there is little matter above to absorb the blue Doppler shifted radiation. The corresponding red peak is absent because of small opacity at the source function maximum and large optical depth due to overlying material. The brightness of the violet peak depends on the height of shock formation. The lower the shock, the higher the density and the larger the source function. The position in wavelength of the bright violet peak depends on the bulk velocity at the shock peak and the width of the atomic absorption prole (described with the microturbulence fudge parameter). The bright grains are produced primarily by waves near and slightly above the acoustic cuto frequency. The precise time and strength of a grain depends on the interference between these waves at the acoustic cuto frequency and higher
THE NON-MAGNETIC SOLAR CHROMOSPHERE 7 Fig. 4. The computed Ca II H line intensity as a function of wavelength and time compared with observations. The leftmost panel shows the unsmeared results from the simulation. In the second panel the simulation has been convolved with a Gaussian point spread function with FWHM of 20 seconds in time and 0.066 A (corresponding to 5 km/s) in wavelength. Scattered light amounting to 1% of the continuum intensity has been added. In the third panel image motion has been simulated by shifting the sequence in time with a random function.
8 MATS CARLSSON AND ROBERT F. STEIN frequency waves. When waves near the acoustic cuto frequency are weak, then higher frequency waves produce grains. The \ve-minute" trapped p-mode oscillations are not the source of the grains, although they can modify the behaviour of higher frequency waves. The wave pattern that exists at the solar surface is due to the interference of many trapped and propagating modes, so that the grain pattern has a stochastic nature. The grain pattern varies with the input velocity eld and the grain appearance is very dependent on the shock strength and shock height. The simulations thus conrm the diagnostic potential of the Ca II H and K resonance lines. To make a proper interpretation of the observations it is, however, necessary to perform selfconsistent radiation hydrodynamic simulations similar to the ones discussed here. For more details the reader is referred to Carlsson & Stein (1997). 4. Observations with SUMER The resonance lines from singly ionized calcium are the best diagnostics of the solar chromosphere available from the ground. The simulations reproduce the observations in these lines remarkably well. It is important that this new dynamic picture of the chromosphere is tested against the space based observations that are now possible with the SOHO satellite. This has been done by Carlsson, Judge & Wilhelm (1997) using the SUMER spectrograph. Spectra around 120 nm were taken with a spatial resolution of 1x2 arcseconds 2 and a temporal resolution of 15-20 s. All continuum observations show very pronounced grain behaviour in the inter-network regions with brightenings on a spatial scale of 3-8 arcseconds and a typical period of 200 s (see Fig. 5). The radiation temperature at 130 nm varies between 4400 K and 5000 K with an rms variation of 86 K. This is consistent with the simulations. The observed spectral lines from neutral carbon, oxygen and nitrogen, on the other hand, show a behaviour dierent from what would be expected from the simulations. The total line emission is strongly varying in time correlated with the continuum intensity variations but with a phase lag consistent with what is expected from propagating waves. However, the lines show emission all of the time in contrast to what would be expected from the simulations. Thus, something important is missing from the calculations { perhaps concerning the fate of shock waves propagating upwards into a magnetic \canopy", perhaps concerning dierent propagation modes (MHD eects), or energetically non-connected material lying along the line of site (like magnetic ux-tubes). 5. Conclusions There is no theoretical or observational evidence for a temperature rise in the magnetic eld free internetwork lower chromosphere. The observed enhanced emission can be produced by temporally varying waves that generate short intervals of high temperatures, without any outward increase in average temperature. Because of the exponential dependence of the Planck function on temperature in the ultra-violet, these short intervals of high temperature dominate the time averaged intensity, even though decoupling of the source function from the Planck function tends to reduce
THE NON-MAGNETIC SOLAR CHROMOSPHERE 9 Fig. 5. Continuum intensity (left), total line intensity (continuum intensity subtracted)(middle), line Doppler shift (right) as function of position along the slit (x-axis) and time (y-axis) for the N I 1319 line (top) and the C II 1334 line (bottom). The continuum intensity is given in counts (top left) and as the corresponding radiation temperature (bottom left). Doppler shifts are shown with upward velocity (blue-shift) bright. All data from the same timeseries.
10 MATS CARLSSON AND ROBERT F. STEIN this sensitivity. Hence, the radiation temperature represents the peaks in gas temperature rather than its mean value. The extra energy that is radiated away comes primarily from the energy dissipated by the wave motions, which goes directly into radiation without passing through a mediating state of enhanced mean thermal energy. One should also be aware that signicant dierences exist between hydrostatic model atmospheres and the average state of a dynamic atmosphere. The presence of waves changes the mean state of the atmosphere, so that procedures that work well in the photosphere may fail badly in the chromosphere. The mean height of formation for lines and continua formed around 1 Mm can vary greatly with time and does not necessarily correspond to the actual layers emitting the photons. Therefore, static formation heights and contribution functions cannot be used for analyzing observations of chromospheric continua and lines from an inherently time-dependent atmosphere. When waves in the chromosphere have large amplitude, linear perturbation theory is not valid since the passage of waves changes the atmosphere fundamentally. Spatially and temporally resolved observations of Ca II H & K lines in internetwork regions show no emission most of the time. Hence, there can be no general chromospheric temperature rise or emission would always be present. Also, high spatial resolution observations of CO emission o the limb show no evidence for a temperature rise in the low chromosphere. Thus, despite long held beliefs, the Sun may not have a chromosphere in the internetwork regions, at least not one with an outward increasing temperature at heights below 1 Mm. The simulations reproduce observations of the resonance lines of Ca II to great detail. The simulations are also consistent with recent SUMER observations of the time-variations of UV contiunua formed around 0.7 Mm. Higher up in the atmosphere the situation seems dierent. Observations of the Mg II resonance lines h & k (Lemaire and Skumanich, 1973, Staath and Lemaire, 1995) indicate that they are in emission all the time. These lines are more opaque than the Ca II resonance lines. SUMER observations likewise show more opaque lines to be in emission all the time, although strongly variable in intensity. The notion of a very dynamic chromosphere thus seems equally valid for the upper chromosphere but there exists either a chromospheric temperature rise at these greater heights or a hotter superimposed component. This latter component may be due to magnetic elements along the line of sight overlying the lower chromospheric inter-network regions. Acknowledgements. Lites, Rutten and Kalkofen are thanked for making available their observations. This work was supported by a grant from the Norwegian Research Council and by grant NAGW-1695 from the National Aeronautics and Space Administration. The computations were supported by a grant from the Norwegian Research Council, tungregneutvalget. References Bocchialini, K., Vial, J.-C., and Koutchmy, S.: 1994, Astrophys. J. 423, L67 Carlsson, M., Judge, P. G., and Wilhelm, K.: 1997, Astrophys. J. Lett. (submitted) Carlsson, M. and Stein, R. F.: 1992, Astrophys. J. Lett. 397, L59
THE NON-MAGNETIC SOLAR CHROMOSPHERE 11 Carlsson, M. and Stein, R. F.: 1994, in M. Carlsson (Ed.), Proc. Mini-Workshop on Chromospheric Dynamics, Institute of Theoretical Astrophysics, Oslo, p. 47 Carlsson, M. and Stein, R. F.: 1995, ApJ 440, L29 Carlsson, M. and Stein, R. F.: 1997, Astrophys. J. 406, 319 Gustafsson, B.: 1973, Uppsala Astr. Obs. Ann. 5, No. 6 Harvey, J., Jeeries, S., Pomerantz, M., and Duvall, T., J.: 1992, BAAS 180, 1705+ Hofmann, J., Steens, S., and Deubner, F. L.: 1996, A&A 308, 192 Lemaire, P. and Skumanich, A.: 1973, Astron. Astrophys. 22, 61 Lites, B. W., Rutten, R. J., and Kalkofen, W.: 1993, Astrophys. J. 414, 345 Rutten, R. J. and Uitenbroek, H.: 1991, Solar Phys. 134, 15 Staath, E. and Lemaire, P.: 1995, Astron. Astrophys. 295, 517 Steens, S., Hofmann, J., and Deubner, F. L.: 1996, A&A 307, 288+ Von Uexkuell, M. and Kneer, F.: 1995, A&A 294, 252