Detectability at different ages

Despite these challenges, there is one thing that can potentially improve the situation: age. Young planets are self-luminous, so instead of reflected light dominating the emission, internal heat will account for the vast majority of light from the planet. The thermal emission of young planets depends on on many factors, but primarily on the formation scenario.

For giant planets, there are two main theories about how they form, referred to as “core accretion” and “disk instability.” We provide a brief description of these scenarios and how they can lead to large boosts in the expected brightness of young planets. Both of models rely heavily on numerical simulations, and have many steps where different physics takes place, governing micron-sized objects up to objects the size of planets. For that reason, we will provide qualitative explanations and summaries of results rather than detailed derivations. For a review of the core accretion and disk instability models see Lissauer & Stevenson (2007) and Durisen et al. (2007).

In the core accretion scenario, dust and small grains stick together in the protoplanetary disk, eventually forming–through some poorly understood process–kilometer sized objects known as plan- etesimals. Collisions between planetesimals cause them to grow larger, eventually forming a plan- etary nucleus. Gas from the surrounding disk will also start to coalesce onto the nucleus once its

7_θ≈λ/D

escape velocity is larger than the average velocity of the gas in the disk. Once the planetesimal reaches 10 Earth masses, it is suspected that a runaway gas accretion occurs, with the planet gain- ing gas as fast as the disk can supply it (see Figure 1.12). This halts once the planet has cleared all the gas within its gravitational reach, forming a (possibly observable) gap in the disk. Core accretion is a “bottom-up” approach, with the entire process taking on the order of a few million years. This process is thought to have led to the formation of planets in the solar system, both the inner ones and the giants, with the inner ones remaining small primarily due to the influence of solar radiation on the formation process.

Figure 1.12: A simulation of the formation of Jupiter, showing the growth in mass and radius as a function of time. Mass grows slowly until the core reaches about 10 Earth masses, at which point runaway gas accretion occurs and the radius contracts rapidly. This figure is taken from Lissauer et al. (2009)

The main competitor to the core accretion theory is formation of giant planets via gravitational instabilities (Boss, 1997). At some phase of evolution, the protoplanetary disk may develop density perturbations causing the formation of spiral structures in the disk. As these spiral structures grow in amplitude and cause supersonic shocks, the disk energy will be converted into heat. If the heat dissipates slowly, the sound speed will rise in the disk and regulate the instability, eventually leading to quasi-stable cycles of heating and cooling. On the other hand, if the heat dissipates very rapidly, the instability will grow and cause fragmentation of the disk into self-gravitating clumps, which will quickly sweep up any gas, dust, and planetesimals nearby. Rather than a slow buildup via core accretion, this process is a “top-down” approach which only takes a few orbits to form a protoplanet, on the order of hundreds to thousands of years, not millions. A key issue is whether these density perturbations are stable or whether they lead to fragmentation in the disk, and this depends on how quickly the disk cools. Numerical hydrodynamics codes are employed to investigate these issues (see Figure 1.13), and consensus is that gravitational instabilities cannot form planets within a few tens of AU of the star, though formation may be possible at larger separations.

Figure 1.13: A numerical hydrodynamics simulation showing the fragmentation of a protoplanetary disk very far from the central star. The figure is taken from Boley (2009).

It may be that these two distinct formation modes are responsible for the formation of giant planets, with core accretion responsible for planets within 100 AU of the star and gravitational instability responsible for very distant giant planets (Boley, 2009). In this case, there should be two separate populations as well, and there is insufficient observational evidence to conclusively verify or refute this. It may also be the case that gravitational instabilities and core accretion work together to accelerate planet formation.

From the perspective of planet detection, there are observable consequences of planet formation, with very different outcomes depending on the formation mechanism (see Figure 1.14). In general, heat from planet formation can amplify the observable self-luminous signature of the planet (Equa- tion 1.36). The disk instability formation mechanism creates a much hotter initial planet, so this is referred to as a “hot-start” model. The core accretion model leads to a colder initial temper- ature, so this is called a “cold-start” model. The temperatures of the planets equilibriate to the same level after a few hundred million years, causing no observable model-dependent temperature discrepancies.

In terms of flux difference, the hot start scenario is much more effective at making the planet detectable (see Figure 1.15), causing a maximum brightness boost of a factor of 100-1000 for young (1 - 5 Myr) planets, regardless of the mass. For the cold start scenario, the boost is more modest, about a factor of 10, and there is hardly any boost for a very massive 10 MJ planet.

Figure 1.14: The evolution of effective temperature and radius of a planet as a function of age, plotted for different mass planets. Note the much higher initial temperature and radii due to the disk instability formation scenario (“hot start”) vs the core accretion (“cold start”) scenario. The effects of planet formation mechanism vanish after a few hundred million years. This figure is taken from Spiegel & Burrows (2012).

Figure 1.15: The evolution of flux in mJy as a function of wavelength, for different ages, for the disk instability (“hot start”, red curves) scenario, and the core accretion (“cold start”, blue curves) formation mechanism. The figure on the right is for a 1 Jupiter mass planet, the one on the right for a 10 Jupiter mass planet. Each curve is an isochrone corresponding to 1, 3, 10, 30, and 100 million year ages, with the younger ages having brighter fluxes. Note the different vertical scales on the left and right figure. The black lines at the top correspond to the J, H, K, L, M, and N infrared bands. This figure is taken from Spiegel & Burrows (2012).

The brightness of the star at different wavelengths, or more precisely the spectrum as a function of age, also affects Fp/F∗ (Equation 1.36). For example, the Hubble extreme deep field had a (5

σ) sensitivity of ∼31 magnitudes9; an Earth-like planet around a Sun-like star 10 pc away would have a brightness of∼30 magnitudes, 2.5 times brighter. Jupiter would be hundreds of times above the noise limit in such an observation, but neither of these planets would be remotely detectable by Hubble. The reason is that the main error source in detecting planets, scattered starlight caused by diffraction and optical errors, scales with the stellar brightness (see Section 1.4.4), hence the

focus on fluxratio. A plot of the wavelength-dependent star-to-planet contrast for various cold- and hot-start models is shown in Figure 1.16.

Figure 1.16: The contrast of various planets compared to a Sun-like star, as a function of wavelength. The red and light blue curves show models similar to those presented in Figure 1.15; three known exoplanets are shown at the top. Jupiter, in pink, is shown at the bottom. Note that the relative contrast seems to reach a peak at around 3.5 - 5 microns, corresponding to the infraredL0 andM0 bands. This figure is taken from Skemer et al. (2014)