We simulated the effect of a stellar flare on the atmosphere of an Earth-like planet located within AD Leo's habitable zone at 0.16 AU. That is the 1 AU equivalent distance for AD Leo, the distance where the planet receives the same integrated energy from AD Leo as Earth does from the Sun (Segura et al.
). Because the simulated atmosphere contains high concentrations of methane, we adjusted the semimajor axis from 0.1595 to 0.1603 AU to give a planetary surface temperature of ~288
K. To model the evolution of the planet's atmosphere during the flare, we modified two existing atmospheric modeling codes to work in a coupled, time-dependent manner. The codes were a radiative-convective model (Pavlov et al.
) and a photochemical model (Segura et al.
). Improved versions of these models were coupled in a time-dependent mode to calculate the changes in temperature, water content, and chemical composition of an Earth-like planetary atmosphere composed of 0.21 O2
. The codes were calibrated so as to closely reproduce the 1976
U.S. Standard Atmosphere, given the conditions of present Earth irradiated by the present Sun ().
FIG. 1. Model results for present Earth around the Sun (dotted lines), compared with vertical profiles from the 1976U.S. Standard Atmosphere (solid lines) and the profiles for the AD Leo planet (dashed lines): (a) temperature, (b) H2O mixing ratio, and (more ...)
The radiative-convective model is actually a hybrid of two separate models. The time-stepping procedure and the solar (visible/near-IR) portion of the radiation code are from the model of Pavlov et al.
). The solar code incorporates a δ two-stream scattering algorithm (Toon et al.
) to calculate fluxes and uses four-term, correlated-k
coefficients to parameterize absorption by O3
, and CH4
in each of 38 spectral intervals (Kasting and Ackerman, 1986
). At thermal-IR wavelengths, we used the independent rapid radiative transfer model (RRTM) implemented by Segura et al.
), based on an algorithm developed by Mlawer et al.
). RRTM uses 16-term sums in each of its spectral bands in which the k
coefficients are concentrated in the areas of most rapidly changing absorption, thereby providing better spectral resolution at altitudes where Doppler broadening is important. Spectral intervals and included absorber species were described by Mlawer et al.
), who fully outlined the method. A disadvantage of this version of the model is that the k
coefficients used therein are not applicable to dense, CO2
-rich atmospheres. This limitation was not a problem for the current study because we restricted our calculations to relatively CO2
-poor atmospheres, such as that of modern Earth. The most recent version of RRTM (http://rtweb.aer.com/
) has been validated up to concentrations of 100 times current CO2
. The (log pressure) grid extended from the assumed surface pressure of 1 bar down to 10−5
bar. The program subdivided this range into 52 levels. Interpolation was required between the climate code and the photochemical code, which ran on a fixed altitude grid. The code worked with a variable time-stepping procedure. Starting from an established value, the code calculated the ensuing time steps based on the difference between the last two temperature profiles: the larger the difference, the smaller the time step. Before the flare the initial time step is 104
s, during the flare it is 50
s, after the flare it is 500
The photochemical model, originally developed by Kasting et al.
), was described by Segura et al.
). This model solves for 55 different chemical species that are linked by 217 separate reactions. The altitude range extends from 0 to 64
km in 0.5
km increments. In the present study photolysis rates for various gas-phase species were calculated by using a δ two-stream routine (Toon et al.
) that accounts for multiple scattering by atmospheric gases and by sulfate aerosols. The model uses the (fully implicit) reverse Euler method to time step to a solution. The initial time step is 10−4
s, and this increases automatically as different species reach equilibrium.
All simulations were performed with a constant planetary surface pressure of 1
atm. The CO2
mixing ratio was kept constant at 355 parts per million per volume (ppmv). Argon was maintained at 1% of the total atmospheric composition. The photochemical model was run with a fixed solar zenith angle of 42°, as this was found to best reproduce Earth's ozone column depth of 0.32
) reported by McClatchey et al.
). Our calibration of the model resulted in an ozone column depth for Earth around the Sun of 8.25
atm-cm). Calculated photolysis rates were multiplied by 0.5 to account for the diurnal cycle. This is a crude approximation for tidally locked M-star planets; however, we assumed that atmospheric mixing between the dayside and nightside would result in some sort of similar averaging. The radiative-convective model used the daytime average solar zenith angle of 60° and the same factor of 0.5 for diurnal variation. The planetary surface albedo was set at 0.2, a number that allows the model to reproduce the temperature profile of present Earth even though clouds are omitted (for a more detailed discussion, see Segura et al.
). The boundary conditions for the photochemical model were fixed surface fluxes for CH4
O, and CH3
Cl, and fixed deposition velocities for H2
and CO. For CH4
, a fixed, relatively low surface flux was used to avoid “methane runaway,” an unrealistic accumulation of methane in the atmosphere. This assumption is to some extent arbitrary; however, it is expected to have little effect on the simulations (see below).
On present Earth, the mechanism that destroys methane in the troposphere is
This process depends heavily on the amount of ozone available in the atmosphere and how rapidly the ozone is photolyzed to form O(1
D). Ozone is produced primarily via the photolysis of oxygen, which occurs at wavelengths <
Å. Ozone itself is photolyzed at wavelengths between 2000 and 8000
Å. In quiescence, AD Leo's UV flux delivers more energy to its planet at 1000–2000
Å than the Sun does to Earth (see ). Consequently, more O2
is photolyzed, and more O3
is produced on the AD Leo planet. The total ozone column depth of the AD Leo planet obtained for this simulation was 1.67
, while Earth's ozone column depth calculated by the same model is 8.25
. In the 2000–3500
Å wavelength range, the opposite happens: AD Leo delivers less energy to its planet than the Sun does to Earth (), so O3
is photolyzed less rapidly. As a result, there are fewer O(1
D) atoms and, accordingly, fewer OH molecules to react with methane. Thus, while our model produces an OH number density of ~106
for present-day Earth, the corresponding value for the AD Leo planet was ~102
. The methane surface flux to reproduce the present Earth methane concentration (1.6
ppm) was calculated by the model to be 7.3
. If this number is used as the boundary condition for methane, CH4
accumulates to concentrations >500
ppm, which is too high to be accurately simulated with our RRTM-based climate model. We chose a constant methane surface flux of 6.4
, or about 88% of the terrestrial value listed above. Given this methane influx, the photochemical code calculates an atmospheric CH4
concentration of 334
FIG. 2. Flux received at the top of the atmosphere of a planet on the AD Leo habitable zone (0.16 AU). The dotted line is the solar flux received by Earth. Times listed on the right lower corner of each panel correspond to the flare fluxes plotted on that panel. (more ...)
To simulate the effect of a stellar flare on a planetary atmosphere, we started from a steady-state solution obtained as described by Segura et al.
), using the AD Leo spectrum during quiescence (black solid line in ). Once the steady solution was reached, the input stellar flux for wavelengths shorter than 4400
Å was changed to that of the stellar flare at a given time. The flare time steps correspond to changes on the input stellar flux () and vary between 91 and 371
s, depending on the time intervals between the available flare spectra. Given a flare time interval, each code ran a different number of time steps according to its own setup and solution method. For example, the first flare interval ran from 0 to 100
s, and its initial conditions are those for the steady state. The photochemical model was run with variable time steps that started at 10−4
s and were increased as the chemical species reached equilibrium. Once the photochemical model reached the flare time step of 100
s, the outputs were saved, and these were passed on to the climate model. The climate model used an initial time step of 50
s, which was then increased until it reached 100
s with use of a variable time step procedure. The outputs of both models at the end of a given flare interval were used as initial conditions for the next time interval. Once the flare ended, the subsequent evolution of the atmosphere was tracked until it reached steady state. We followed an algorithm similar to that used during the flare, but the AD Leo flux was held constant in the quiescent state. This allowed larger time steps to be used during the recovery phase.