Caleb K. Harada, M.A.

The Transiting Exoplanet Survey Satellite, or TESS, is revolutionizing exoplanet astronomy by surveying almost the entire sky for the faint signals of exoplanets transiting their host stars. So far, TESS has helped scientists discover hundreds of exoplanets (and many more planet candidates), adding to the over 5,000 confirmed exoplanets discovered to date.

Interactive plots displaying properties of exoplanets discovered with TESS using public data from the NASA Exoplanet Archive. Planet system position and distance information is shown in the top "Astrometry" panel. Physical planet and host star properties are shown in the bottom two panels labeled "Planet Mass-Period Diagram" and "Stellar HR Diagram," respectively. Plots were made using Tableau.

Stellar spectra are integral to nearly all aspects of modern astrophysics, as they allow us to learn about a star's physical properties as well as its radial velocity and evolutionary stage. The following animations show a generative data-driven model that predicts what a stellar spectrum should look like for a given set of stellar properties (e.g., temperature, surface gravity, and elemental abundances). The model (2nd-order polynomial in the 5 labels) was trained on data from the APOGEE Survey at the wavelength-pixel level, closely following the procedure of Ness et al. 2015.

The first movie shows how the spectrum changes as a star evolves off the main sequence and ascends the red giant branch ("RGB"). The metallicity is fixed to solar metallicity, while logg varies from 3.5 to 0.5 and Teff simultaneously varies such that the star moves along an isochrone. The second movie shows how the same region of the spectrum changes with metallicity at fixed Teff and logg. Clearly, both spectra show deeper absorption lines as the metallicity increases (with all other parameters fixed) or as the star moves up the RGB at fixed composition. So how can one tell the difference between a cool, low-logg star and a warmer, higher-logg star that is more metal-rich? The key is to look at the relative strengths of the absorption lines. As the metallicity at fixed stellar parameters increases, so does the optical depth of the stellar atmosphere, which subsequently increases the strength of all the absorption lines somewhat uniformly. However, when a star ascends the RGB, the physical mechanism for changing absorption line strength is the decrease in effective temperature, which alters the ionization state of the atmosphere (as described by the Saha Equation ). This sets the the atomic line strengths---at higher temperatures, more atoms can become ionized due to thermal collisions. When this happens these atoms can no longer absorb photons, thus decreasing the strength of absorption lines. Therefore, decreasing Teff increases the strength of absorption lines, but not all lines are affected equally because different atoms will have different ionization states at a given temperature.

This animation of a simulated hot Jupiter was originally published in Harada et al. (2021) to complement a suite of simulated high-resolution emission spectra.

The color scale indicates the temperature at the vertical level in the atmosphere corresponding approximately to the IR photosphere pressure (∼26 mbar). The gray-shaded area shows the integrated optical depth of clouds above the IR photosphere, with more opaque regions corresponding to thicker clouds. The red (and blue) contours show the net positive (and negative) line-of-sight velocities (in increments of 1 km/s) caused by atmospheric winds and the planet’s rotation at the IR photosphere level. The black dot indicates the antistellar point and the black "x" indicates the substellar point. The subplot on the left-hand side shows the location of the planet in its orbit as seen from the perspective of a distant observer, indicated by the triangle.

Under certain conditions in a three-body system, a dynamical phenomenon known as the Kozai Mechanism can cause a distant third body to dramatically affect the orbit of an otherwise stable inner binary. On a timescale much longer than the orbital period, the perturbing third body drives a periodic exchange between the inner system's eccentricity and inclination. This process may be an important factor in planet evolution and migration, and may be a key factor in explaining how hot Jupiters form.

The first animation shows a three-body simulation from the rest-frame comoving with the system's center-of-mass, with two massive "stars" in orbit around each other and a test particle orbiting the inner, more massive star. The axes show the spatial scale in AU and the timescale is shown at the top. The masses and orbital parameters of all three bodies were selected to optimize viewability for the purpose of the demostration. The second animation shows the same simulation, only transformed into the rest-frame of the more massive central star. Here, it becomes apparent that the orbit of the test mass is perturbed by the outermost star and we can see the periodic changes in the inclination and eccentricity of its orbit (remember, this is a numerical simulation!).

Here are a few more N-body simulations created with the same software used above. As before, the axes shown the spatial scale in AU and the timescale is shown at the top of each animation.

The first animation depicts the TRAPPIST-1 system, a distant solar system with at least seven terrestrial planets orbiting a cool M-dwarf sun. The second animation shows a hypothetical exoplanet system with two planets in stable orbits around a central binary star. (A real example of such a configuration is the circumbinary planet Kepler-16b.) The third animation shows a hypothetical planet on a chaotic trajectory through a binary star system. The planet is ultimately ejected from the system.

Another interesting result of the restricted three-body problem, in which two orbiting masses are much more massive than the third, is the existence of five Lagrange points. At each of the Lagrange points, the forces due to the gravity of the two larger bodies and the centrifugal pseudoforce exactly balance out. Therefore, in the co-rotating frame of the two massive bodies, a less massive object placed at any of the Lagrange points will remain stationary (note, however, that the stability of the Lagrange points requires more careful consideration of the Coriolis pseudoforce).

This animation shows the 3D surface of the effective potential felt by a massless particle in the rotating frame of the Earth-Moon system. The mathematical form of the effective potential is $$\phi_{eff}(\vec{r}) = -\frac{G M_1}{|\vec{r} - \vec{r}_1|} - \frac{G M_2}{|\vec{r} - \vec{r}_2|} -\frac{1}{2} \frac{G(M_1 + M_2)}{|\vec{r}_2 - \vec{r}_1|^3} |\vec{r}|^2$$ where $M_1$, $\vec{r}_1$ and $M_2$, $\vec{r}_2$ are the masses and positions of the Earth and Moon respectively and $\vec{r}$ is measured from the center of mass. The first two terms are the gravitational potential and the third term is the centrifugal pseudopotential. Here, the effective potential is plotted in log space for contrast, and a 2D contour plot of the potential is projected onto the bottom of the figure. The larger and smaller black circles represent the positions of the Earth and Moon, and the blue points show the five Lagrange points (i.e., where the gradient of the potential is zero).

Simple stellar populations (SSPs) are key compoments of models of galactic evolution and can be useful for visualizing the evolution of a coeval population of stars (e.g., a cluster). By definition, an SSP is a group of stars born at the same time with the same initial composition. The distribution of the stars' masses is defined by the initial mass function (IMF). As an SSP evolves over time, the most massive stars die off first, followed by less massive stars. This leads to the overall reddening and dimming of the population over time, as well as the subsequent chemical enrichment of the surrounding ISM by exploding high-mass stars.

This simulation shows the evolution of a solar-metallicity SSP assuming a Kroupa IMF with one million stars, along with an HR diagram of the stars within the population. The SSP, shown here for ages ranging from 100 Myr to 10 Gyr, was simulated using the ArtPop package and individual frames were compiled into a gif using FFmpeg. The spatial distribution of stars was modeled using a Sersic profile with a Sersic index of 0.8, effective radius of 250 pc, and ellipticity of 0.3. The observations were simulated in the R, V, and B filters for a 10-meter class telescope. Notice the apparent reddening and increase in apparent magnitude of the population as stars toward the high-mass end of the main sequence evolve and die off.