What is granulation in astronomy

On a somewhat larger scale, convergence is toward particularly strong downdrafts, associated with the mesogranulation. Where these downdrafts occur, the granules tend to be smaller and to move laterally into the downdraft. Over the broad mesogranular upflows the granules tend to be larger. This behavior is confirmed by local correlation tracking of observed granules Muller et al.

We now consider the thermodynamic properties of granulation in relation to the granule structure. The temperature of the plasma is controlled by the balance between convective transport and radiative losses. The temperature, entropy, and density of the plasma near the solar surface have approximately bimodal distributions. The downward-moving intergranular lane plasma has low temperature, low entropy, very low ionization, and high density.

The upward-moving granule plasma has high temperature, high entropy, high ionization, and low density Figs. The temperature, entropy, and ionization are closely coupled.

Below the surface, upflows occupy of the area and downflows. One result of these bimodal distributions is that the edges of granules are extremely sharp with very steep gradients in temperature, entropy, and hydrogen ionization. Figure 12 shows the temperature and emerging intensity along a horizontal slice through two granules. Note that granule edges are much steeper in temperature at a given geometric depth than in emergent intensity.

Below the surface, the entropy is very nearly constant in the ascending fluid, while it is highly fluctuating in the descending fluid Fig. The entropy fluctuations in the descending fluid are initiated at the surface, where fluid that visits the photosphere along different paths is cooled by different amounts. While descending, the cold fluid is highly turbulent and is being mixed with overturning, higher entropy fluid, increasing the fraction of the mass that comes from fluid that overturns without having visited the surface.

Thermal diffusion with their higher entropy surroundings also heats the filamentary downdrafts. The mean entropy of the descending fluid thus increases steadily with depth Fig. Near the surface, the divergence of the convective, radiative, and kinetic energy fluxes are large, but the sum of the divergence of all three is small, and vanishing on the average if exotic terms such as viscous flux are neglected.

The radiation cooling time near the solar surface is very short of the order of seconds , so the fluid energy balance adjusts very rapidly. Since the dominant H - opacity is very temperature sensitive T 10 , it produces an extremely steep vertical temperature gradient near the surface Fig. The temperature gradient is much larger in the ascending flow K km -1 than in the mean structure 30 K km -1 The smaller value for the average gradient comes about because the steep temperature drop in ascending flows occurs at different depths in different granules and because the temperature rise in the downdrafts occurs at larger depths and is more gradual than in the updrafts.

Above the surface, the fluid is nearly in radiative equilibrium, with a little radiative heating balancing expansion cooling over granules and a little radiative cooling balancing compressional heating in the converging flow over the intergranular lanes. Changes due to the convective motions are a small perturbation on this basic structure. Energy transport switches from convective below the surface to radiative above the surface.

The fluid is always approximately in radiative-convective equilibrium for the atmospheric structure through which it is moving. The upflows transfer their internal energy to radiation between optical depths 30 and 1. Their temperature gradient is slightly less than the radiative equilibrium value because the radiative flux is increasing as the optical depth decreases due to the transfer of energy from convection to radiation.

This well-known gradient on an optical depth scale corresponds to an extremely steep gradient on a geometric depth scale Fig. A Lagrangian perspective, following a fluid parcel, of this Eulerian behavior, is presented at the end of this section. As a result, there is a much wider spread in temperatures K at a given geometric depth just below the surface; Fig.

This clearly reveals the crucial role of radiation in controlling the structure of the solar surface and the closeness of the atmosphere at each point on the surface to instantaneous radiative equilibrium near local optical depth unity.

Thus, even though it is tempting to believe that plasma is monotonically cooling as it overturns in the visible photosphere, that is not a correct picture. The overturning plasma is actually close to radiative equilibrium at all times and is often being heated, rather than cooled, by radiation as it traverses the optically thin layers. Near the surface, upflows and downflows transport approximately equal amounts of energy.

With increasing depth the downflows come to dominate the energy transport. Driving of the convective flows comes primarily from the intergranular lanes and downdrafts.

The buoyancy forces driving the convective motions are significantly larger in the downflows than in the upflows, below the surface, because the entropy fluctuations are much larger in the downflows, which contain fluid that reached the surface and lost entropy by radiation Figs. The downflows drive the broad, cellular upflows indirectly, through mass conservation, by displacing the warm, entropy-neutral, ascending material.

With increasing depth these downflows merge into more widely spaced downdrafts, to form a treelike structure. Correspondingly, the upflows develop a larger scale quasi-cellular structure with increasing depth an "inverse cascade". Alternatively, one can view this as the operation of a "normal" convective instability, where the medium is a plasma permeated by granular scale downdrafts.

Because of the cooler downdrafts that are superposed on the isentropic background, the mean state is slightly superadiabatic and hence convectively unstable. This initiates motions in the form of diverging upflows and converging downflows, on scales much larger than the scales of the granular fluctuations. Tracing the history of a typical fluid parcel Lagrangian perspective; Fig.

It cools, its opacity drops, and photons can escape more easily, increasing the cooling rate. This is a situation with significant positive feedback. A slight drop in temperature greatly reduces the dominant H - opacity and hence the optical depth, so that the radiative losses increase, which further reduces the parcel's temperature, and so on. A runaway temperature drop results. Radiation carries away the energy and entropy of the fluid parcel in about 20 s.

An ascending parcel's temperature drop is so rapid K s -1 that its density increases above the average for its depth, whereupon gravity and an adverse pressure gradient relative to the mean slow its vertical motion and the high pressure pushes it horizontally.

The horizontal deflection shows up as a brief period of large strain without any significant vorticity. The parcel moves along the surface toward an intergranular lane at shallow optical depth for a minute or two. It continues emitting and absorbing radiation, with a small net effect of a little radiative reheating as the fluid passes above a warm granule. This keeps the fluid, which would otherwise cool adiabatically to a very low temperature as it expands into the low-density photosphere, near but slightly below the radiative equilibrium temperature.

The entropy increases slightly during this period. Parcels that pass through the unit optical depth surface reach heights that average about km and typically stay above the surface for 3 minutes. On reaching a cool intergranular lane, the local radiation equilibrium temperature suddenly drops. The plasma parcel cools, its density increases further, and buoyancy pulls it down.

The plasma parcel now heads down into the interior. As it turns down it typically passes through a region of both large vorticity and large strain. There is no more radiative heating or cooling during its descent. Unless the parcel is inside a major downdraft, thermal diffusion in the cool intergranular lanes which become very narrow with increasing depth raises its entropy as it descends.

Eventually, diffusion decreases and the parcel descends with a more gradual increase of entropy. Those parcels in the interior of major downdrafts keep their low surface entropy longer because they do not experience as much diffusive thermal energy exchange.

Granules evolve because their diverging flow pushes against neighboring granules and because overlying cool fluid splits them apart. Above a granule, high pressure, due to higher temperature and larger scale height, diverts the flow horizontally, producing a fountain-like topology. The horizontal flow encounters surrounding expanding granules against which it pushes.

They are caused by the convective motions of the hot gases inside the Sun. Sometimes called rice grain or lemon peel, this textured appearance is due to hot gas continually boiling up to the Sun's surface, cooling, and sinking down again.

The pattern of large cells seen in the sun's chromosphere , when viewed in the light of the strong emission line of ionized hydrogen. At this point turbulent convective motions occur, similar to a pot of boiling water. See also sudden commencement. Cellular structure of the photosphere visible at high spatial resolution.

Individual granules, which represent the tops of small convection cells, are to km in diameter and have lifetimes of 8 to 10 minutes.

What you are actually seeing is a process known as convection, which is like a boiling pot of water where heat is brought from below the pot to the surface the steam you see. An extremely luminous star of large diameter and low density. No supergiant s are near enough to establish a trigonometric parallax. Fortunately, there are examples of convection that fit into a classroom. An excellent example can be seen in hot Japanese Miso soybean paste soup.

While it is known that the darker appearance of the umbra and penumbra is due to their lower temperatures, the sharpness of the boundaries between the umbra and penumbra, and between the penumbra and photosphere, is a phenomenon that is not yet properly understood.

While sunspots, especially large ones, can be fairly long-lived their lifetimes being measured in weeks and months , they do eventually disappear, often by successive fragmentation into smaller and smaller sunspots. Likewise, sunspots do not suddenly appear fully grown, but usually show up as small structures, irregularly shaped and usually without a penumbra darker structures without penumbra are usually referred to as pores , and grow within days or sometimes weeks to their full size.

In the end, the uncertainty on the radius is calculated by dividing the maximum by the minimum matching radii. Table 8 reports the intrinsic incertitude on the planet radius for all the prototypical planets of Table 3 and for representative wavelengths of Table 2. This uncertainty is given either for the envelope of the various computed transits Col.

It is strongly related to the rms reported in Table 5 : the optical region returns larger errors as well as larger rms than those at the infrared wavelength, while the uncertainty is larger for terrestrial planets while their rms is smaller up to 0.

The Sun returns higher values for the radius error than the K dwarf. The solid red and blue curves correspond to radially symmetric stellar limb-darkened disks with different planet radii to match the maximum red and minimum blue green shading. It should be noted the duration of the transits used in this work Table 3 reach up to seven hours.

In our analysis, longer transit durations may lead to lower but still significant estimates for the radius uncertainty.

The effects of the granulation noise on the radius are non-negligible and should be considered for precise measurements of exoplanet transits of, in particular, planets with small diameters. The actual granulation noise is quantified in the next section. The full characterization of the granulation is essential for determining the degree of undertainty on the planet parameters.

In this context, the use of 3D RHD simulations is important for estimating the amplitude of the convection-related fluctuations. This can be achieved by performing precise and continuous observations of stellar photometry and radial velocity, which are interpreted with RHD simulations, before, after, and during the transit periods. Table 8 Radius and uncertainty due to the granulation fluctuations for the different prototype planets of Table 3 and 3D RHD simulations of Table 1.

The aim of this section is to investigate how the granulation behaves across the different wavelength bands of Table 2. For this purpose, we used the transit light curve of three representative granulation stellar disks in the optical and near-infrared region. Following the limb-darkening procedure explained in Sect. For each wavelength bin, we then subtracted the light curve generated with the granulation from the smoothed limb-darkening one. Since we did not include the atmosphere in our prototype planets, the resulting signal is the noise caused by granulation.

The colors denotes different wavelengths ranges Table 2 in the optical top panel and in the near infrared bottom panel. The relative difference is obtained subtracting, for each wavelength range, the light curve generated with the granulation snapshot with the one computed with the appropriate radially symmetric stellar limb darkened disk see text.

Figure 14 quantifies the deviations from the smoothed limb-darkening transit caused by the granulation as a function of wavelength. Figure 14 also displays a correlation among the different wavelength ranges in the visible and the infrared regions, at least for the spectral resolution used in this work.

Higher spectral resolution in the wavelength bands is probably needed to isolate the contribution of the granulation effect on the stellar spectral lines. A more complete analysis on this aspect will be presented in a future work.

We used 3D RHD surface convection simulations with the S tagger code to provide synthetic stellar-disk images to study the background granulation during planet transits of three prototype planets: a hot Jupiter, a hot Neptune, and a terrestrial planet.

We analyzed the effect of convection-related surface structures at different wavelengths ranging from the optical region to the far-infrared. These wavelength bands cover the range of several ground- and space-based telescopes observing planet transits and are sensitive to molecules that can give important hints on the planetary atmosphere composition. We modeled the transit light curves using the synthetic stellar-disk images obtained with the spherical-tile imaging method that was previously explained and applied in Chiavassa et al.

We used the data size, flux, and duration of the transit of three prototype planets with the purpose of studying the resulting noise caused by the granulation on the simulated transits. From the synthetic light curves, our statistical approach shows that the granulation pattern of solar and K-dwarf-type stars have a non-negligible effect on the light-curve depth during the transit for small and large planets.

This intrinsic uncertainty affects the determination of the planet transit parameters such as the planet radius up to 0. The consequences of the granulation noise on the radius are non-negligible. The full characterization of the granulation is essential to determine the degree of uncertainty on the planet parameters. In this context, the use of 3D RHD simulations is important to estimate the amplitude of the convection-related fluctuations. This can be achieved by performing precise and continuous observations of stellar photometry and radial velocity, explained with RHD simulations, before, after, and during the transit periods.

We identified two types of noise that act simultaneously during the planet transit: the intrinsic change in the granulation pattern with timescale e. We showed that the rms caused by the granulation pattern changes in the stellar irradiation during the transit of the terrestrial planet between 3. This indicates that our modeling approach is reliable.

Finally, the granulation noise appears to be correlated among the different wavelength ranges in the visible and the infrared regions, at least for the spectral resolution used in this work. Three-dimensional RHD simulations are now established as realistic descriptions for the convective photospheres of various classes of stars. They have recently been employed to explain the transit of Venus in Chiavassa et al.

Their light-curve fit was supported by the fact that the granulation pattern changes would affect transit depth. Modeling the transit light curve of exoplanets is crucial for current and. The good and time-dependent representation of the background stellar disk is mandatory. In this context, 3D RHD simulations are useful for a detailed quantitative analysis of the transits.

The authors thank the referee for helping in finding a numerical problem during the refereeing process. Transiting curve data for the terrestrial prototype planet of Table 3 and the RHD simulations of Table 1 at different inclination orbital angles inc.

Radius and uncertainty due to the granulation fluctuations for the different prototype planets of Table 3 and 3D RHD simulations of Table 1. Scatter plot of 42 top and 12 bottom different transit light curves for a terrestrial and hot Jupiter planet of Table 3 , respectively.

Same as in Fig. Example of limb-darkening fit red line with the Claret law see text to the averaged intensity profiles of Fig. Enlargement from Fig.

Granulation noise for three representative granulation stellar disk realizations of the Sun affecting the central part of the light curve for a terrestrial planet Table 3.