Limits on the Auroral Generation of H₃⁺ in Brown Dwarf and Extrasolar Giant Planet Atmospheres with the Keck Near Infrared Echelle Spectrograph

A major goal in exoplanet studies is understanding the diversity and evolution of planetary atmospheres, including atmospheric responses to variable stellar environments and loss rates over time. Within this goal, describing the thermodynamic properties and energy budgets that govern atmospheric temperatures, chemistry, and expansion are paramount. As the interface between an atmosphere and its surrounding space, the upper atmospheres of planets, including the thermosphere, ionosphere, and exosphere, are excellent laboratories to probe atmospheric thermodynamics as they are more sensitive to changes in the energy flow than lower atmospheric regions.

In the past decade, planetary upper atmospheres outside our solar system have begun to be probed by spectroscopic observations of hot Jupiters and brown dwarf planetary analogs. Notably, atmospheric expansion and hydrodynamic escape, as well as thermospheric and ionospheric layers, temperatures, and winds, have all been measured or inferred for exoplanets using tracers such as He i and Na i, among others (see Spake et al. 2018; Allart et al. 2019; Seidel et al. 2020; Cauley et al. 2021). Recently, observations of ionospheric species have been described as evidence for the possible first detection of an exoplanetary magnetic field Ben-Jaffel et al. (2021).

A direct and potentially significant tracer of the ionosphere, which has yet to be detected in an extrasolar planetary mass object, is the molecular ion H₃ ⁺. H₃ ⁺ is expected to form readily in the upper atmosphere via the ionization of H₂ by extreme-ultraviolet radiation (EUV; 10–100 nm), or by energetic electrons precipitating along field lines during aurorae:

$$\begin{eqnarray*}&&{{\rm{H}}}_{2}+{\rm{h}}\nu \to {{\rm{H}}}_{2}^{+}+{{\rm{e}}}^{-}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{{\rm{H}}}_{2}+{{\rm{e}}}^{-* }\to {{\rm{H}}}_{2}^{+}+2{{\rm{e}}}^{-}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{{\rm{H}}}_{2}+{{\rm{H}}}_{2}^{+}\to {{\rm{H}}}_{3}^{+}+{\rm{H}}.\end{eqnarray*}$$

Destruction of H₃ ⁺ then occurs by dissociative recombination, or, in the lower thermosphere by reaction with other molecular species, such as hydrocarbons or H₂O. Thus, H₃ ⁺ is expected to only exist in concentration above the homopause where atmospheric mixing is weak and abundances of heavier species are low. In stellar atmospheres, H₃ ⁺ is not expected to be abundant except in the coolest, metal-poor stellar atmospheres (Tennyson & Miller 2001), such that any detection in a stellar environment can be attributed to a planetary ionosphere.

Within the thermospheres and ionospheres of giant planets and brown dwarfs, H₃ ⁺ is expected to be a dominant source of radiative cooling that scales with the incoming energy flux, sometimes called the "H₃ ⁺ thermostat" (Maillard & Miller 2011). Observations of Jupiter's auroral regions have shown that H₃ ⁺ rotational-vibrational emission in the near- and mid-infrared effectively balances variable energy input from EUV flux, the solar wind, and particle precipitation. Its role as a coolant is expected to continue for extrasolar giant planets, at least up to high thermospheric temperatures less than ∼10,000 K, above which the formation will be suppressed by the dissociation of H₂ (Koskinen et al. 2007). In our own solar system, observations of H₃ ⁺ in Jupiter, Saturn, and Uranus have been a useful diagnostic of upper atmospheric temperatures, densities, wind dynamics, and cooling, as well as magnetosphere–atmosphere interactions (see a review by Miller et al. 2020).

Theoretical predictions for H₃ ⁺ emission in close-in giant planet and brown dwarf atmospheres agree that the emission is likely to be orders of magnitude larger than that emitted by Jupiter. This increase can be driven by elevated EUV flux compared to Jupiter in the case of giant exoplanets, or by powerful magnetic fields and associated aurorae for brown dwarfs or exoplanets with strong magnetospheres. While there is consensus that H₃ ⁺ emission is an important thermal mechanism, exactly how much stronger emission is to be expected in these environments is uncertain. Early predictions suggested that a planet like τ Boo b may have an H₃ ⁺ emission luminosity upward of 10¹⁷ W, roughly 10⁵ × that of Jupiter (Miller et al. 2000), with most of that energy concentrated in a few lines. Subsequent models, however, have been conservative, with Koskinen et al. (2007) predicting a maximum total luminosity for any planet of 10¹⁵ W and Chadney et al. (2016) predicting maximum total luminosities of around 10¹⁶ W for a planet like HD 209458 b between 0.1 and 0.2 au away from a young, active K or M dwarf. An additional complication is that individual line strengths do not grow linearly with the total intensity as the thermosphere becomes hotter, as more molecular transitions become populated at higher excitation temperatures. Furthermore, none of these models account for auroral contributions to H₃ ⁺ generation, which may boost the H₃ ⁺ luminosity depending on the auroral energy deposition.

Free-floating brown dwarfs may represent the best environment for successful H₃ ⁺ detection as a number of them possess evidence of powerful aurorae (10⁴ × more energetic than Jupiter's) in the form of electron–cyclotron maser (ECM) emission and, in a few cases, synchronous variable Balmer emission (Hallinan et al. 2015; Pineda et al. 2016). The auroral current is postulated to be driven by either the break between corotating and subrotating magnetic field lines outside the dwarf (Nichols et al. 2012), or by interaction with a brown dwarf satellite (Hallinan et al. 2015). By assuming that the strength of the aurorae corresponds to a linear increase in the number of precipitating electrons, and that the energy of the electrons do not increase significantly, Helling & Rimmer (2019) have suggested that H₃ ⁺ emission will similarly be near or above 10⁴ × that of Jupiter (10¹⁶–10¹⁸ W). Pineda (2017) argues that if brown dwarf aurorae operate analogously to that of Jupiter, then H₃ ⁺ L' emission of H₃ ⁺ could carry up to 10 × more energy than optical Balmer emission that has been associated with aurorae for some nearby brown dwarfs (up to 10¹⁸ W). These works suggest that detection of H₃ ⁺ emission from a free-floating brown dwarf with current instruments is plausible.

A number of attempts have previously been made to detect H₃ ⁺ emission in hot Jupiters, most of which have focused on observing the fundamental rovibrational H₃ ⁺ lines in the L band around 4 μm (Brittain & Rettig 2002; Goto et al. 2005; Shkolnik et al. 2006; Laughlin et al. 2008; Lenz et al. 2016). Shkolnik et al. (2006) carried out a survey of six systems hosting extrasolar giant planets (EGPs) with the CSHELL instrument on the NASA Infrared Telescope Facility and set the lowest detection limit so far of 6.3 × 10¹⁷ W for GJ 436 at 1σ significance. Most recently, Lenz et al. (2016) observed the HD 209458 system with the Very Large Telescope (VLT) Cryogenic high-resolution InfraRed Echelle Spectrograph (CRIRES) using occultation spectroscopy to attempt to reduce the effect of the stellar background. They achieved a 3σ detection limit of 5.3 × 10¹⁸ W for the Q(3,0) line at 3985.5 nm but were significantly hampered by poor weather.

There has been one observational attempt to detect H₃ ⁺ emission in brown dwarfs. Pineda (2017) searched for H₃ ⁺ lines in K-band, medium-resolution spectroscopy of brown dwarfs with known ECM radiation using the Keck Multi-Object Spectrometer For Infra-Red Exploration. They did not detect any excess infrared emission attributable to H₃ ⁺ but did not set emission limits for these objects. Within their discussion, they suggest high-resolution L-band spectra to confirm their results, as only about 10% of H₃ ⁺ emission is expected in K, with the remaining energy emitted mostly in L (Neale et al. 1996). Therefore, a high-resolution search for emission lines in the L band to set observational limits is of high interest despite the added challenge of increased thermal background when observing at longer wavelengths.

In this paper, we describe a search for H₃ ⁺ emission in five brown dwarfs and five systems hosting giant planets using the Keck Near Infrared Echelle Spectrograph (NIRSPEC). We describe our target selection methodology in Section 2. Section 3 outlines our observations of the 10 targets and our data reduction process. In Section 4, we present results and set upper limits on emission for each of our targets. We interpret our nondetections in the context of atmospheric and magnetospheric models for brown dwarfs and giant planets in Section 5 and finally discuss future paths for detection with observatories such as the James Webb Space Telescope (JWST).

The primary goal of our study is to attempt to constrain the upper atmospheric and auroral chemistry of brown dwarfs by setting observational emission limits for H₃ ⁺. As an additional goal, we attempt to detect or set upper limits for H₃ ⁺ in giant exoplanets at distances of 0.1–0.2 au from solar- or later-type dwarfs, which models suggest are the most promising planetary targets (Koskinen et al. 2007; Chadney et al. 2016). In determining a number of targets to observe, we attempted to balance the integration time per target with the sample size so that we would reasonably avoid nondetection due to small number statistics.

To select our brown dwarf targets we relied upon radio observations of ultracool dwarfs summarized in Williams (2018). At present, approximately a dozen brown dwarfs have been observed emitting ECM radiation, which is thought to be produced by auroral processes and is similar to auroral radio emission observed from the poles of Jupiter. We chose the closest brown dwarfs with observed ECM radiation, and which span the spectral range from the end of the main sequence to T dwarfs. H₃ ⁺ emission has only been previously modeled in one brown dwarf (2MASSI J1835379+325954; Helling & Rimmer 2019). Therefore, we decided to select targets with diverse spectral types and therefore atmospheric conditions rather than those that necessarily had the most intense ECM radiation, as the optimal atmospheric conditions for high H₃ ⁺ emission in brown dwarfs is still mostly unexplored. We also selected the ultracool dwarf binary system 2MASS J07200325-0846499 (Scholz's star) as it is possible that the binarity helps stimulate aurorae and H₃ ⁺ generation as Io does with Jupiter by producing an interacting plasma (Connerney et al. 1993), although it is not clear if the separation in this system (a ∼ 2.2 au; Dupuy et al. 2019) is close enough for a similar phenomenon to occur. We do not independently consider the inclination or rotation rates of the dwarfs, although inclinations have been measured for some dwarfs (e.g., Vos et al. 2017) and may affect aurorae observability (although this has not been quantified). Our four selected brown dwarf systems can be found in Table 1.

The motivation for an additional search for H₃ ⁺ in exoplanets is that of three previous observational attempts, two have focused on only one ultrahot Jupiter each (τ Boo b, Laughlin et al. 2008; and HD 209458 b, Lenz et al. 2016). While detection of H₃ ⁺ in any planet is at the current limits of technical capability, models published after these observations (Chadney et al. 2016) suggest that the thermospheres of these specific EGPs are very likely too hot to contain significant H₃ ⁺ abundance. Therefore, we decided to include a number of planetary systems that are cooler, yet still have a high ionizing flux from their host star.

To select planetary targets, we used the NASA Exoplanet Archive (DOI 10.26133/NEA12). Confirmed planets were sorted based on the semimajor axis, bolometric flux received, mass (or $M\sin i$), and distance from Earth. We excluded planets with masses less than that of Saturn, where the thermospheric composition is expected to begin to change from being hydrogen and helium dominated. Planets with semimajor axes less than 0.07 au were excluded based on the probability that their thermospheres are too hot to contain H₃ ⁺ through previously described dissociation processes. Otherwise, increased proximity to the star and bolometric flux received were considered to make targets better candidates, as those planets are simply exposed to more ionizing radiation. In reality, it is the EUV, XUV, and X-ray flux received that is most important for H₃ ⁺ production, not the bolometric flux, but EUV and XUV are not measured for most exoplanet systems—due to a lack of observatories in this wavelength region and because of absorption from the interstellar medium—so the less-informative bolometric flux is used as a proxy. Systems with multiple EGPs were preferred even if some of those giant planets are not necessarily good candidates for detection. As the signal-to-noise ratio of our spectra is of central importance to emission limits, the apparent magnitude was used as a primary selection criterion. It is for the same reason that all of our targets are nontransiting systems detected through radial velocity measurements, as known transiting planets farther than 0.1 au from their host stars are still generally much farther from Earth due to the lower probability of having a transiting orbital inclination at increased semimajor axis. The fact that they are nontransiting precludes the possibility of using more sophisticated observational techniques like occultation spectroscopy to search for H₃ ⁺.

Our five selected planetary targets can be found in Table 2. A comparison of the estimated EUV flux that some of these planets receive compared to that of Jupiter and a few other exoplanetary systems is shown in Figure 1. This figure illustrates that we are probing a parameter space between the extremes of thermospheres that are too hot, and too little ionizing EUV radiation to produce observable H₃ ⁺. EUV flux estimates come from the X-exoplanets database (Sanz-Forcada et al. 2011), which uses coronal modeling to predict EUV if no observational data are available. These values should be viewed as orders of magnitude. In particular, the EUV flux received by planets around GJ 876 is probably an order of magnitude higher as the star is an active M dwarf.

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Table 2. Observed Planetary Target Sensitivity Limits

Object	Spectral Type	Dist. (pc)	K Mag	itime (min)	Emission Limit (W)		Planet	$M\sin i$ (MJ )	a (au)
					Q(1,0)	Q(3,0)
GJ 876 (1)	M3.5V	4.68	5.01	20.5	2.2 × 1017	6.8 × 1017	c	0.76	0.134
					4.7 × 1017	5.2 × 1017	b	2.39	0.214
HD 192263 (2)	K1/2V	19.64	5.54	67.0	2.3 × 1018	3.2 × 1018	b	0.73	0.153
55 Cancri (3)	K0V	12.59	4.01	40.0	7.4 × 1018	8.4 × 1018	b	0.80	0.113
					1.6 × 1018	1.4 × 1018	c	0.16	0.237
							d	3.12	5.957
HD 217107 (4)	G8V	20.07	4.54	64.2	2.9 × 1018	8.7 × 1018	b	1.39	0.075
							c	4.09	5.94
υ Andromedae (5)	F9V	13.49	2.86	21.2	2.9 × 1018	5.1 × 1018	b	0.69	0.059
					2.5 × 1018	1.0 × 1019	c	13.98	0.828
							d	10.25	2.513

Note. Stellar spectral types, distances, and magnitudes come from the SIMBAD astronomical database (Wenger et al. 2000). Stellar radial velocity references: (1) Fouqué et al. (2018), (2–5) Gaia Collaboration (2018). Planetary ephemeris references: (1) Millholland et al. (2018), (2) Dragomir et al. (2012), (3) Bourrier et al. (2018), (4) Giovinazzi et al. (2020), (5) Piskorz et al. (2017). itime refers to the integration time on target not including read times or observing overheads.

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As a third target class, we chose to observe the white dwarf–brown dwarf (WD-BD) binary GD 1400. This novel target class may combine the benefits of planetary and brown dwarf targets for H₃ ⁺ emission. The brown dwarf may have a strong magnetic field and aurorae, but it also receives strong EUV flux from the white dwarf. The white dwarf is dimmer than main-sequence stars in the mid-IR, so the system will have a lower stellar contrast. Unfortunately, GD 1400 is very faint despite being the closest WD-BD binary known and is a thus an extremely challenging target for L-band high-resolution spectroscopy.

All together, we selected 10 promising targets for the detection of H₃ ⁺ in the atmosphere of a planetary mass object. Highest observational priority was given to brown dwarf 2MASSI J1835379+325954, as it has the strongest evidence for an aurora and is the only brown dwarf with a published model for H₃ ⁺. Otherwise, the observing time was based primarily on object observability and scheduling constraints for a given night. Observations of these objects are described in the next section.

We observed a total of two and a half nights with Keck/NIRSPEC (McLean et al. 1998; Martin et al. 2018; López et al. 2020) on the 10 targets described in Section 2. Individual observations occurred on 2020 August 27, September 3, October 6, and 2021 March 3, UT.

Spectra were obtained using the high-resolution mode with the KL filter. The echelle and cross-disperser angles were set to 6225 and 3372, respectively. This setup places six H₃ ⁺ lines within order 19 of the echellogram with a wavelength range of approximately 3.94–4.02 μm. These are the same lines included in previous searches by Shkolnik et al. (2006) and Lenz et al. (2016), and which have also been observed prominently in Jupiter (e.g., Maillard et al. 1990). Of these six lines, the Q(1,0) and Q(3,0) transitions, at 3953.0 and 3985.5 nm, respectively, are expected to be the most intense, with the Q(1,0) being most intense at lower rotational and vibrational temperatures akin to Jupiter (∼500 K) and Q(3,0) becoming dominant at higher temperatures (∼2000 K; Neale et al. 1996). Other transitions in the R and P branch do reach similar intensities as these lines; however, the region around 4 μm is the densest region of prominent lines across low and high excitation temperatures, and other prominent lines could not be observed with a single echelle setting.

Each night, we chose the slit width to be comparable to the average seeing in order to balance the target throughput by minimizing the sky background. The best seeing we achieved on any night was around 04, so only the 0432 × 12'' (R ∼ 25,000) and wider slits were used. There was no appreciable cloud cover on any night listed above. The precipitable water (PW) ranges for our nights were 1 to 1.2 mm for 2020 August 27, 0.6 to 1 mm for 2020 September 3, 4–6 mm for 2020 October 6, and 0.5–0.65 mm for 2021 March 3.

All observations used a standard ABBA nodding pattern along the slit that allows removal of thermal background by A–B pair subtraction. At the beginning and end of observing each science target, we observed at least one spectroscopic standard star of A0 or adjacent spectral type, and at similar elevation to the target, for use in correcting telluric lines. Exposure times were chosen for each target to be safely below detector nonlinearity at ∼20,000 ADU. Except for the brightest stellar targets, the exposure time is generally limited by the thermal background itself with an exposure of 30 s per coadd nearing nonlinearity.

The observation parameters for each target are detailed in Tables 1 and 2. As discussed in Section 2, our observation strategy attempted to balance sensitivity with the number of targets observed. Thus, no target is observed on sky for longer than 2.5 hr, corresponding to a maximum integration time of about 90 minutes with readout and nod overheads. Due to target visibility and scheduling constraints, most targets are not observed at this limit.

Initial data reduction steps, including calibration, order rectification, trace fitting, and spectral extraction, were carried out using a modified version of the Python pipeline described by Piskorz et al. (2016). Modifications were made for bad-pixel correction to prevent clipping with our data. This pipeline uses the optimal extraction methods described in Horne (1986). Stated simply, optimal extraction improves the spectral signal-to-noise ratio by weighing pixels based on the wavelength averaged point-spread function. Reduction steps are carried out individually for each nod pair for bright targets. For dimmer targets, it was sometimes necessary to combine adjacent pairs together, essentially as a coadd, so that the spectral trace could be well fit. Our faintest target, WD-BD binary GD 1400, is sufficiently dim that nearly all pairs must be added to confidently fit the trace.

Raw 1D science spectra are continuum normalized before being combined into a median spectrum. Continuum normalization is achieved by smoothing the spectrum with a Gaussian filter and then constructing a polynomial fit between local maxima, which trace the average continuum level that is then divided out. This normalization routine changes the systematic structure of the spectra but not at the scale of the expected H₃ ⁺ emission lines.

Wavelength calibration is performed by a second-order fit of sky emission-line positions in the observation data to the same lines in atmospheric transmission models by Lord (1992). Line centers are determined by a Gaussian fit. We find that even with the spectrograph angles set to the same positions each night, there is still a variation of about 10 Å in the wavelength position of a given pixel between nights. The average rms deviation of measured sky line positions compared to our preferred wavelength solutions is 1.1 pixels, with the most accurate wave solution for HD 217107 (rms∼0.37 pixels) and the least accurate for LSPM J0036+1821 (rms∼1.6 pixels). For reference, the expected FWHM of any H₃ ⁺ line is ∼4 pixels.

We use ESO's molecfit tool for telluric correction of the science spectra (Kausch et al. 2015; Smette et al. 2015). Molecfit creates a synthetic transmission spectrum using a radiative transfer code and local observatory and meteorological data. Synthetic telluric correction is preferable to using standard stars alone as the synthetic spectrum is theoretically noiseless, whereas standard stars necessarily contain photon noise in addition to any systematic errors that can exist in both synthetic and observed spectra. For each target, we generate a synthetic telluric spectrum by fitting a molecfit spectrum to the corresponding standard star. The atmospheric model used is the molecfit default. The exception is that we additionally fit the molecule NO₂. The most significant absorption features observed within our wavelength range are caused by NO₂. This coincidence is beneficial, as NO₂ is expected to have less atmospheric temporal variation compared to other molecules, notably H₂O. For planetary targets, we take the additional step of using the best-fit telluric model from the standard stars and using it as the start for an additional molecfit refinement using the science spectrum itself. This step is not possible for brown dwarfs as their intrinsic spectra contain too many absorption lines for molecfit to be able to reliably disentangle the telluric features. An additional benefit of using molecfit that we utilize is a final refinement of the wavelength solution based on the synthetic model.

As a test for systematic errors that molecfit might introduce to our spectra, we experimented with performing fits using different standard stars for the target GJ 876 (multiple standard stars were observed around this data set). After comparing fits from three different standard stars fit separately, there are no systematic differences of large enough magnitude or at a spectral scale to alter the interpretation of the corrected spectrum. Therefore, while some systematic errors are likely introduced by molecfit, we do not believe they could be responsible for an erroneous positive or negative detection.

For our planetary targets, we expect that the radial velocity does not vary significantly compared to our resolution over our roughly two-hour periods of observation. Therefore, we expect the H₃ ⁺ line positions to remain effectively stationary so that no spectral shift and add technique is necessary.

In the next section, we describe our search for H₃ ⁺ lines within the data, and our method for setting observational limits for H₃ ⁺.

After data reduction, we search for candidate H₃ ⁺ lines within our spectra, and in the absence of any, set limits on the line luminosities that we would have expected to detect given our spectral signal-to-noise ratio.

For all our targets, we elect to take the simple approach of a direct, visual search near the anticipated H₃ ⁺ line positions based on the object radial velocities and after correcting for Earth's barycentric velocity. For exoplanetary systems, we also need to account for the radial velocity of each planet, which is dependent on the orbital inclination and phase at observation. Fortunately, most of these exoplanets have relatively well-characterized orbits with known inclinations and precise ephemeris data. For example, the uncertainty in the orbital positions of GJ 876 b and c are less than 1%. In cases where the inclination of the planet is not known, we simply calculate the range in line positions given a minimum and maximum possible radial velocities (RV) at the time of observation.

Theoretically, we could perform a cross-correlation approach for planetary targets that would be independent of the known planetary RV, either by correlating a H₃ ⁺ line model with our combined spectra, or by correlating our spectra at either end of a target's observation sequence to try to catch the slight change in RV of the planet over that time period. We do not believe, however, that either of these options would result in an increased sensitivity. The primary reason is that we only expect a few lines to have intensities that are greater than our spectral noise, and cross-correlation techniques perform best when many lines are available. Also, models of H₃ ⁺ line intensities from the ionospheric environment are dependent on non-LTE considerations. If our line models do not account for this correctly it could lead to erroneous results. As for measuring the change in the planetary RV, the maximum change in the RV of any planet over the observation period is of the order of ∼1 km s⁻¹, or ∼0.5 Å, which is at the edge of our resolution capability. Finally, by correlating spectra at different points in the observation we necessarily reduce the signal-to-noise ratio of the individual spectra, which makes it less likely that the H₃ ⁺ emission will rise above the stellar and thermal background and successfully be correlated.

The spectra for targets 2MASSI J1835379+325954 and GJ 876 are shown in Figures 2 and 3, with wavelength ranges set to expected line locations. The top panel shows the science and telluric model produced by molecfit before the telluric correction has been applied, and the bottom panel shows the spectrum after the telluric model has been divided out of the science spectrum. Note that, while the brown dwarf spectra do have as high signal-to-noise ratios as stellar spectra, the observed variability is partly due to closely spaced absorption lines from various species in the brown dwarf atmosphere and is not purely noise. The spectra for all other targets are provided in appendix figures.

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We do not detect any candidate H₃ ⁺ emission in any of our brown dwarf or planetary targets. Although some targets have a local maximum near one or two line positions, these are all low significance. Specifically, while 2MASSI J1835379+325954 has several low-significance maxima at predicted line locations, it does not have any peak at the Q(1,0) line, which is expected to be the second-strongest observed line in our wavelength range at a wide range of excitation temperatures.

To calculate emission limits for each target, we follow a similar procedure as in previous searches by Shkolnik et al. (2006) and Lenz et al. (2016). Our limits are calculated individually for the Q(1,0) and Q(3,0) lines, as these are expected to be the most intense. First, we calculate the standard error of the normalized mean science spectrum in each wavelength bin. Next, if the predicted line location is precisely known (as in the case for brown dwarfs and planets with known inclinations), we calculate both the median of the standard error and the standard deviation of the spectrum within the expected FWHM of an H₃ ⁺ line, approximately 4 pixels. To ensure our sensitivity estimate is conservative, we use whichever value is larger as the uncertainty in the spectrum at that location. In almost all cases, the standard deviation of the spectrum in the binned wavelength region is higher than our estimate of the standard error from individual exposures within the same region. If the line locations do not have a precise prediction, we calculate the same metrics within the entire region where the line may appear. The theoretical line width of an H₃ ⁺ line is calculated from the instrument profile (an output of molecfit) and Doppler broadening. Despite the fact that all of our brown dwarf targets are likely rapid rotators (P < 3 hr), H₃ ⁺ emission from auroral generation is expected to be concentrated toward the poles (as in Jupiter; see latitude profile in Drossart 2019) such that at our resolution, the line width is still dominated by the instrument profile. We assume that our synthetic telluric spectrum is noiseless, which is one of the major benefits of using a synthetic model. Next, we estimate the L' magnitude for each target (if no L' photometric measurements are available) using K–L' colors derived from Bessell & Brett (1988) for main-sequence stars or by using colors from brown dwarfs with similar spectral types to our targets published in Golimowski et al. (2004). This estimated L' magnitude and its associated uncertainty are then converted to a flux density in the region of our H₃ ⁺ lines, and then to a luminosity density given the target parallax. We scale our spectral uncertainty to the luminosity within the line profile and assume that we would follow up any peak greater than 3σ significance to get our average line sensitivity for the target.

Our brown dwarf sensitivities are plotted in Figure 4. Planetary sensitivities are shown in Figure 5 against sensitivities from previous observational attempts and limits from theoretical studies. Brown dwarf sensitivities are roughly an order of magnitude or more stringent than any upper limits previously set for giant exoplanets, which is primarily a result of their low luminosity. We achieve the highest sensitivity for any planetary target so far for GJ 876 c, with a sensitivity of 2.2 × 10¹⁷ W for the Q(1,0) line. All calculated sensitivities are compiled in Tables 2 and 1.

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In this section, we discuss the physical interpretation of our nondetection for the properties of brown dwarf and giant planet atmospheres and magnetospheres. We will examine brown dwarfs and giant planets separately, beginning with brown dwarfs.

5.1. Auroral Mechanisms in Brown Dwarf Atmospheres

5.2. Extrasolar Giant Planets

5.3. Prospects for Future H₃ ⁺ Detection in Brown Dwarfs

In this study, we have presented a search for H₃ ⁺ emission from brown dwarfs with evidence of aurorae and select systems hosting giant planets at semimajor axes of 0.1 to 0.2 au. The key results are as follows.

• 1.  
  We do not detect any H₃ ⁺ emission, but set the first upper limits for H₃ ⁺ emission from free-floating brown dwarfs, which, to our knowledge, have never been searched with high-resolution spectroscopy.
• 2.  
  Our upper limits for H₃ ⁺ emission from brown dwarfs range between 2.7 and 9.3 × 10¹⁶ W, within the upper range of a plausible detection based on models.
• 3.  
  Our nondetection in brown dwarfs suggests that the aurora-like processes occurring in these objects are probably not analogous to those of Jupiter, namely that electron beams are not able to generate a H₃ ⁺ density proportional to the energy of these phenomena. An order-of-magnitude increase in sensitivity is needed to probe this hypothesis further.
• 4.  
  We set the lowest upper limit for H₃ ⁺ emission in a giant exoplanet yet, with a limit of 2.2 × 10¹⁷ W. Despite these limits, we are not able to place additional constraints on giant exoplanet atmospheres or magnetospheres.
• 5.  
  We suggest that brown dwarfs are the best targets for future H₃ ⁺ detection attempts and show that JWST will be able to reach emission limits around an order of magnitude deeper than current ground-based instruments with equal exposure time.

The authors thank Quinn Konopacky for reviewing and providing helpful feedback on the draft of this manuscript.

The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.

The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

Facilities: Keck:II (NIRSPEC).

Software: Numpy (van der Walt et al. 2011), Pandas (McKinney 2010), Scipy (Virtanen et al. 2020), Astropy (Price-Whelan et al. 2018).

Figures 6–12 contain additional spectra of our observed targets.

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