To the students I've worked with along the way, thank you for always reconnecting me to the joy of math and science, even when it was hard to find in my research. Many thanks to the Blake band members who have been with me through all the highs and lows of the past five and a half years.
INTRODUCTION
2017 and apparently the case for the giants of the solar system (e.g. Owen et al., 1999) – it could in fact be the solid composition that could encode evidence for the formation locations of planets (e.g. Öberg & Wordsworth, 2019) . High-dispersion coronagraphy (HDC) was presented as a collaboration between HCI and high-resolution spectroscopy (e.g., Sparks & Ford, 2002; Wang et al., 2017).
MULTI-EPOCH OBSERVATIONAL APPROACH AND SIMULATION FRAMEWORK
- Introduction
- Direct Planetary Detection Methods
- Multi-Epoch vs. CRIRES Approaches
- Comparison to Other Techniques
- Simulations
- Summary
In contrast, the multi-epoch approach uses shorter (∼2–3 hours) observations, where the planetary line-of-sight velocity is constant and a single-velocity measurement can be made (the dots each represent a single epoch). ). The lack of time variation in the planetary signal from the multi-epoch data makes it more difficult to distinguish between the telluric and stellar signals than with the CRIRES approach.
SIMULATING THE MULTI-EPOCH DIRECT DETECTION TECHNIQUE TO ISOLATE THE THERMAL EMISSION OF THE
NON-TRANSITING HOT JUPITER HD187123B
Introduction
The multi-epoch method (e.g., Lockwood et al., 2014), rather than searching for shifting planetary lines in a single night, observes at several epochs around the planet's orbit for ∼2–3 h per epoch. Because the multi-epoch technique does not require the planetary lines to move within a short period, it is applicable to the future study of planets at larger orbital radii, including those in habitable zones.
NIRSPEC Observations and Data Reduction ObservationsObservations
1998 and the most updated Keck/HIRES radial velocity dataset was analyzed by Feng et al. We use the ESO tool Molecfit (Kausch et al., 2014) to fit the initial telluric model to each night of data.
Simulating NIRSPEC Observations
While this would not make much of a difference to the detection capability of the simulations, it will be important for detecting the planet in the real data (described in Section 3.4). The spectra are then broadened according to the instrument profiles that fit the data and are interpolated on the wavelength axes for each of the orders and nights.
NIRSPEC Data Analysis and Results
Panels B-H of Figure 3.3 show the log probabilities of each of the combined nights using each of the three CC-to-log(L) approaches: Zucker log(L) (blue), Zucker ML (green), and Brogi & Line (maroon). One difference between the simulated results and the data results is the size of the log probability variation.
Data
Star-Only Correlation
- Planet Mass [M 1.3 J ] 0.6
- Discussion
- Conclusion
- Appendix
We also note that the simulations seem to show a larger increase towards 0 km/s than the data suggests. By fitting the simulations to the results, we can remove unintended structure in the probability surface.
PRIMARY VELOCITY AND ORBITAL PHASE EFFECTS ON PLANETARY DETECTABILITY FROM SMALL EPOCH
NUMBER DATA SETS
Introduction
To do this, we consider the effects of primary (stellar) velocities and orbital phases at each epoch. The planetary velocity is similarly composed of the dynamical radial velocity (which, unlike the stellar RV, is large enough to be resolved by NIRSPEC), the systemic velocity, and the barycentric velocity.
Methods
Segments of data (eg, orders and pieces of orders after saturated telluric pixels are masked) are cross-correlated separately and converted to log-likelihood functions to be combined. Once the two-dimensional cross-correlation for each epoch is converted to a two-dimensional (stellar and planetary velocity offsets) log-likelihood surface, the planetary log-likelihood intercept is taken from the measured stellar velocity.
Primary Velocity Simulations
We generate 100 sets of five-epoch simulations with randomly selected orbital phases for each of the five primary velocity groups. The particularly low 𝑅2 values of the four primary velocity groups except for the near-zero reflect the high levels of structured noise.
Comparison to Data
We note that the simulations predict a much larger improvement going from the largest absolute primary velocity case to the near-zero primary velocity case (1.1 to 4.4) than seen in the data (1.4 to 1.7). Because the planetary velocities are closer to the telluric frame in the near-zero primary velocity group (both because
Number of Epochs
This could explain why random primary velocity simulations do not benefit from multiple epochs to the same extent as near-zero primary velocity epochs. While the heights of the Gaussian peaks from the near-zero primary velocity pool increase from 5- to 10-epoch simulations, the 10-epoch random primary velocity simulations would have a slightly worse placement of primary velocities than the 5-epoch case.
Stellar Properties
The near zero primary velocity simulations are shown in light blue and the random primary velocity simulations are shown in green. Water signatures arising in cooler stars may increase the need for carefully selected near-zero primary velocity epochs.
Discussion
We also see considerable similarity between the heights derived from the examples of random primary velocities across temperatures and stellar radii. Simulations of near-zero primary velocity are shown in light blue, and simulations of random primary velocity are shown in green.
Conclusion
The two key parameters that can be selected with the choice of observing nights are the primary velocity (due to the variable barycentric velocity) and the planetary orbital phase. Furthermore, for near-zero primary velocity epochs, the closer their orbital phases are to quadrature, the better the constraints on 𝐾𝑝 will be.
Appendix
In each subplot, the red dashed line corresponds to the primary velocity during this period, and the black dashed line corresponds to 𝑣𝑠𝑒 𝑐 given by 𝐾0. If it were on the edge, on the other hand, 𝑣𝑠𝑒 𝑐 would fall on the other side of the white range of possible planetary speeds.
Introduction
2016 reported the Keplerian orbital velocity of HD 88133 b as 40±15 km/s using 6 epochs of NIRSPEC𝐿band data and 3 epochs of𝐾band data. 2017 reported the Keplerian orbital velocity of ups And b as 55±9 km/s using 7 epochs of NIRSPEC 𝐿band data, 3 epochs of 𝐾𝑙 band data covering the left half of the NIRSPEC detector, and 3 epochs covering the 🝐 band data covers right half of the detector.
Standard Multi-Epoch Analytic Approach
Thus, while the corrected simulations shown in the bottom panel of Figure 5.2 provide an optimistic view of possible detections with the 6 separate epochs of the NIRSPEC1.0 𝐿 band presented in Piskorz et al. Most of the structured noise arising in the simulations presented here and in Buzard et al.
Upsilon Andromedae b
The stellar spectral model used to analyze the ups and 𝐿 band data in Piskorz et al. This result is encouraging because it means that NIRSPEC2.0 would allow multi-phase detection of ups And b with the exact seven periods presented in Piskorz et al.
Discussion
2021, with near-zero primary velocities, they could have offered a very strong detection and a chance for further atmospheric characterization (e.g. Finnerty et al., 2021). The upgrade to the NIRSPEC instrument will provide a significant advantage for multi-epoch planetary detection, due to the increases in both resolution and spectral grip (Finnerty et al., 2021).
Conclusion
CHOICES ALONG THE MULTI-EPOCH ANALYTIC PATHWAY
Introduction
Physical Considerations Planetary Orbital PositionPlanetary Orbital Position
If the observation center is in quadrature, Δ𝑣𝑠𝑒 𝑐 = 0 because the planet starts and ends with a common velocity. The barycentric velocity is the fraction of the Earth's orbital motion in the direction of the target system.
Instrumental Considerations Wavelength RegionWavelength Region
Whether the planetary signal crosses detector pixels during an observation depends on the instrumental resolution and the change in planetary line-of-sight motion over the observation (as described in Section 6.2). If we then plug in Equation 6.2 for the change in the planetary line-of-sight velocity, we can relate the number of pixels we want the planetary signal to cross (𝑛𝑝𝑖𝑥) to the required resolution (𝑅), given parameters of the system (𝐾𝑝 , 𝑃ℎ𝑟) and observation (ℎ𝑜 𝑏 𝑠, 𝑀𝑐𝑒𝑛𝑡 . 𝑜 𝑏 𝑠.
Analytic Considerations Wavelength CalibrationWavelength Calibration
The small differences between these two routines completely change the shape of the planetary log-likelihood curves. The planetary log-likelihood curves come from the cuts across the peak of the stellar correlation in each data segment.
Summary
If this were the case, the jack-knife errors, which do not distinguish between epochs that should be better/worse able to be constrained, would be overestimated and could cause the planetary peak to appear with more confidence lower than it actually is from the data. A more realistic error analysis would calculate the expected ability of each epoch to bound, which can be approximated by the orbital position of the epoch.
NEAR-INFRARED SPECTRA OF THE INFLATED POST-COMMON ENVELOPE BROWN DWARF NLTT5306B
Introduction
Although NLTT 5306 B does not fill its Roche Lobe, near-IR spectra of SpeX on IRTF have shown evidence of a mean gravity, with log(𝑔) ∼4.8, indicating that the brown dwarf is inflated (Casewell et al ., 2020a). As a known thick disk object (Steele et al., 2013), NLTT 5306B is at least 5 Gyr (the minimum cooling time of the white dwarf) and probably much older.
NIRSPEC Observations and Data Reduction ObservationsObservations
To correct for the sky emission lines in the data, we chose to incorporate them into our cross-correlation analysis rather than split them out. This was consistent with the core required to extend a SkyCalc model to fit the sky emission lines in our data from all three nights.
Brown Dwarf Spectral Models
The internal temperatures and heat distributions together determine the effective temperature of the irradiated brown dwarf. The effective temperatures are closely clustered around the inner temperatures because the irradiance is relatively mild due to the low white dwarf effective temperature.
Cross-Correlation Analysis
We can use previous information from this system to figure out what to expect for the Keplerian orbital velocity of the brown dwarf, 𝐾. An upper limit on the brown dwarf mass of 75 MJup would correspond to a lower limit on 𝐾.
Results
The center and rightmost panels of Figure 7.3 show the example fit to only day epochs and only night epochs, respectively. Comparisons of the full set of Sonora 2021 models with our datasets—all epochs, day epochs, and night epochs—are shown in Figure 7.4.
- Discussion
The effective temperature on the day side being higher than the effective temperature on the night side and the brightness temperatures could be explained if the hotspot was only visible on the day side of the brown dwarf. The presented 2020a could come from a linear combination of the higher gravity brown dwarf and lower gravity material.
