A new way to see inside black holes

Black holes are real astrophysical objects, but their interiors are hidden and can only be "observed" through mathematics. The structure of rotating black holes is typically illustrated with the help of special coordinates. But any such coordinate choice necessarily results in a distorted view, just as the choice of projection distorts a map of the Earth. The truest way to depict the properties of a black hole is through quantities that are coordinate-invariant. We compute and plot all the independent curvature invariants of rotating, charged black holes for the first time, revealing a landscape that is much more beautiful and complex than usually thought.Comment: 4 pages, 3 figures, published in Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture (Phoenix, AZ: Tessellations Publishing, 2015), 479-482. Revised to fix a referenc

Moderate-resolution K-band Spectroscopy of Substellar Companion κ Andromedae b

We present moderate-resolution (R ~ 4000) K-band spectra of the "super-Jupiter," κ Andromedae b. The data were taken with the OSIRIS integral field spectrograph at Keck Observatory. The spectra reveal resolved molecular lines from H₂O and CO, and are compared to a custom PHOENIX atmosphere model grid appropriate for young planetary-mass objects. We fit the data using a Markov chain Monte Carlo forward-modeling method. Using a combination of our moderate-resolution spectrum and low-resolution, broadband data from the literature, we derive an effective temperature of T_(eff) = 1950–2150 K, a surface gravity of log g = 3.5–4.5, and a metallicity of [M/H] = −0.2–0.0. These values are consistent with previous estimates from atmospheric modeling and the currently favored young age of the system (<50 Myr). We derive a C/O ratio of 0.70_(-0.24)^(+0.09) for the source, broadly consistent with the solar C/O ratio. This, coupled with the slightly subsolar metallicity, implies a composition consistent with that of the host star, and is suggestive of formation by a rapid process. The subsolar metallicity of κ Andromedae b is also consistent with predictions of formation via gravitational instability. Further constraints on formation of the companion will require measurement of the C/O ratio of κ Andromedae A. We also measure the radial velocity of κ Andromedae b for the first time, with a value of −1.4 ± 0.9 km s⁻¹ relative to the host star. We find that the derived radial velocity is consistent with the estimated high eccentricity of κ Andromedae b

Moderate-resolution K-band Spectroscopy of Substellar Companion κ Andromedae b

We present moderate-resolution (R ~ 4000) K-band spectra of the "super-Jupiter," κ Andromedae b. The data were taken with the OSIRIS integral field spectrograph at Keck Observatory. The spectra reveal resolved molecular lines from H₂O and CO, and are compared to a custom PHOENIX atmosphere model grid appropriate for young planetary-mass objects. We fit the data using a Markov chain Monte Carlo forward-modeling method. Using a combination of our moderate-resolution spectrum and low-resolution, broadband data from the literature, we derive an effective temperature of T_(eff) = 1950–2150 K, a surface gravity of log g = 3.5–4.5, and a metallicity of [M/H] = −0.2–0.0. These values are consistent with previous estimates from atmospheric modeling and the currently favored young age of the system (<50 Myr). We derive a C/O ratio of 0.70_(-0.24)^(+0.09) for the source, broadly consistent with the solar C/O ratio. This, coupled with the slightly subsolar metallicity, implies a composition consistent with that of the host star, and is suggestive of formation by a rapid process. The subsolar metallicity of κ Andromedae b is also consistent with predictions of formation via gravitational instability. Further constraints on formation of the companion will require measurement of the C/O ratio of κ Andromedae A. We also measure the radial velocity of κ Andromedae b for the first time, with a value of −1.4 ± 0.9 km s⁻¹ relative to the host star. We find that the derived radial velocity is consistent with the estimated high eccentricity of κ Andromedae b

Radial Velocity Measurements of HR 8799 b and c with Medium Resolution Spectroscopy

High-contrast medium resolution spectroscopy has been used to detect molecules such as water and carbon monoxide in the atmospheres of gas giant exoplanets. In this work, we show how it can be used to derive radial velocity (RV) measurements of directly imaged exoplanets. Improving upon the traditional cross-correlation technique, we develop a new likelihood based on joint forward modeling of the planetary signal and the starlight background (i.e., speckles). After marginalizing over the starlight model, we infer the barycentric RV of HR 8799 b and c in 2010 yielding −9.2 ± 0.5 km s⁻¹ and −11.6 ± 0.5 km s⁻¹, respectively. These RV measurements help to constrain the 3D orientation of the orbit of the planet by resolving the degeneracy in the longitude of an ascending node. Assuming coplanar orbits for HR 8799 b and c, but not including d and e, we estimate Ω = 89°⁺²⁷₋₁₇ and i = 20°.8^(4.5)_(-3.7)

Medium Resolution Spectroscopy of the HR 8799 planets

High-contrast medium resolution spectroscopy has been used to detect molecules such as water and carbon monoxide in the atmospheres of directly imaged gas giant exoplanets. Improving upon the traditional cross-correlation technique, we develop a new likelihood based on joint forward modelling of the planetary signal and the starlight background (i.e., speckles). We show how it can be used to better characterize the atmosphere of directly imaged exoplanets and measure their radial velocity (RV). After marginalizing over the starlight model, we infer the barycentric RV of HR 8799 b and c in 2010 yielding -9.2 ± 0.5 km/s and -11.6 ± 0.5 km/s respectively. These RV measurements help to constrain the 3D orientation of the orbit of the planet by resolving the degeneracy in the longitude of ascending node. Assuming coplanar orbits for HR 8799 b and c, but not including d and e, we estimate the longitude of ascending node to be 89o (+27,-17) and the inclination to be 20.8o (+4.5, -3.7)

Medium Resolution Spectroscopy of the HR 8799 planets

High-contrast medium resolution spectroscopy has been used to detect molecules such as water and carbon monoxide in the atmospheres of directly imaged gas giant exoplanets. Improving upon the traditional cross-correlation technique, we develop a new likelihood based on joint forward modelling of the planetary signal and the starlight background (i.e., speckles). We show how it can be used to better characterize the atmosphere of directly imaged exoplanets and measure their radial velocity (RV). After marginalizing over the starlight model, we infer the barycentric RV of HR 8799 b and c in 2010 yielding -9.2 ± 0.5 km/s and -11.6 ± 0.5 km/s respectively. These RV measurements help to constrain the 3D orientation of the orbit of the planet by resolving the degeneracy in the longitude of ascending node. Assuming coplanar orbits for HR 8799 b and c, but not including d and e, we estimate the longitude of ascending node to be 89o (+27,-17) and the inclination to be 20.8o (+4.5, -3.7)

Medium Resolution Spectroscopy of the HR 8799 planets

High-contrast medium resolution spectroscopy has been used to detect molecules such as water and carbon monoxide in the atmospheres of directly imaged gas giant exoplanets. Improving upon the traditional cross-correlation technique, we develop a new likelihood based on joint forward modelling of the planetary signal and the starlight background (i.e., speckles). We show how it can be used to better characterize the atmosphere of directly imaged exoplanets and measure their radial velocity (RV). After marginalizing over the starlight model, we infer the barycentric RV of HR 8799 b and c in 2010 yielding -9.2 ± 0.5 km/s and -11.6 ± 0.5 km/s respectively. These RV measurements help to constrain the 3D orientation of the orbit of the planet by resolving the degeneracy in the longitude of ascending node. Assuming coplanar orbits for HR 8799 b and c, but not including d and e, we estimate the longitude of ascending node to be 89o (+27,-17) and the inclination to be 20.8o (+4.5, -3.7)