Multi-Object High-Resolution Transmission Spectroscopy

• Mo-HRTS is an observing mode that simultaneously records high-resolution line-resolved and low-resolution broadband transmission spectra using multiple comparison stars.
• It leverages advanced instrument architectures and ADC corrections to stabilize the continuum, effectively mitigating calibration degeneracies and telluric variations.
• Mo-HRTS enables detailed exoplanet atmospheric characterization by linking line-resolved spectroscopic features with broadband transit signals.

Multi-Object High-Resolution Transmission Spectroscopy (Mo-HRTS) is a time-series observing mode in which high-resolution spectra of a transiting exoplanet host star are recorded simultaneously with spectra of many comparison stars within the same field. In its broader observational and analysis form, it exploits multi-object, high-resolution echelle spectrographs to obtain, from a single time series, both high-resolution line-resolved transmission spectra and low-resolution broadband transmission spectra, using simultaneous reference stars to provide a quasi-absolute flux calibration of the continuum at high resolution while tracking instrumental and telluric common-mode systematics. The mode therefore sits at the intersection of transmission spectroscopy, multiplexed fiber-fed spectroscopy, differential spectrophotometry, and instrument designs that can preserve chromatic coupling and wavelength stability over multi-hour transit baselines (Magrini et al., 2023, Bestha et al., 23 Sep 2025, Bestha et al., 2023).

1. Conceptual basis and distinction from conventional HRTS

Traditional ground-based HRTS commonly continuum-normalizes each echelle order, divides in-transit spectra by out-of-transit spectra, and then applies further low-order or spline-based normalizations. In the formulation used for Mo-HRTS studies, the observed high-resolution transmission spectrum can be written as

$$F_{\mathrm{obs}}(\lambda,t)=c(t,\lambda)\,F_{\mathrm{model}}(\lambda,t)+\epsilon,$$

where $c(t,\lambda)$ absorbs the unknown continuum normalization as a function of time and wavelength, including blaze-function drifts, fiber/slit losses, telluric transparency changes, and chromatic throughput. Removing or marginalizing $c(t,\lambda)$ preserves line shapes and Doppler information, but it sacrifices sensitivity to the absolute continuum level and its slope, thereby entangling abundance, reference pressure $p_0$, cloud opacity $\kappa_{\mathrm{cloud}}$ or cloud-top pressure $P_{\mathrm{cloud}}$, and $R_p/R_*$. Mo-HRTS addresses this by using simultaneous reference stars to stabilize the continuum and by extracting a low-resolution transmission spectrum

$d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$

from the same dataset used for the line-resolved analysis, so that the continuum anchors the high-resolution retrieval rather than being divided away (Bestha et al., 23 Sep 2025).

A recurrent misconception is that any simultaneous second fiber already constitutes Mo-HRTS. The sodium survey with HARPS and HARPS-N makes the distinction explicit: two fibers per exposure were used, with the target on fiber A and fiber B used simultaneously for sky or a calibration source, and “This is not multi-object science multiplexing, but it is a simultaneous reference channel.” In that survey, targets were observed sequentially, one planet per night. By contrast, Mo-HRTS requires simultaneous science spectra of the target star and one or more comparison stars within the same field, so that telluric and instrumental references are intrinsic to the science exposure rather than reconstructed across epochs (Langeveld et al., 2022).

2. Instrument architectures and field-dependent optical implementation

The most explicit instrument concept developed specifically for Mo-HRTS is the TMT/HROS multi-object mode. TMT provides an $f/15$ final focus with a plate scale of $2.18\ \mathrm{mm/arcsec}$ on a curved, non-telecentric focal plane with diameter $c(t,\lambda)$0 and radius of curvature $c(t,\lambda)$1. Image quality degrades across the $c(t,\lambda)$2 field due to field aberrations, with geometric radius increasing from $c(t,\lambda)$3 on-axis to $c(t,\lambda)$4 at $c(t,\lambda)$5 off-axis even before atmospheric effects. HROS accommodates multi-object high-resolution spectroscopy with $c(t,\lambda)$6 fibers at $c(t,\lambda)$7; the baseline multiplex is six objects for full $c(t,\lambda)$8–$c(t,\lambda)$9 coverage, and by blocking subsequent echelle orders up to $c(t,\lambda)$0 objects could be fed to the slit/IFU. The architecture embeds, inside each fiber positioner, a pick-off mirror, a compact collimator, the ADC, and a reimaging camera, with a planned $c(t,\lambda)$1 microlens conversion for efficient coupling and a planned dichroic splitter behind the camera to route blue and red channels while retaining compactness per positioner (Bestha et al., 2023).

The ADC itself is a counter-rotating, achromatic Rotational ADC composed of two amici-prism doublets. The prism materials are Nikon N-7054 and CaF2, the clear aperture is $c(t,\lambda)$2 diameter per prism, and the optimized apex angles are $c(t,\lambda)$3, $c(t,\lambda)$4, $c(t,\lambda)$5, and $c(t,\lambda)$6. ZEMAX Multi-Configuration optimization yielded representative relative counter-rotation settings of $c(t,\lambda)$7 at $c(t,\lambda)$8, $c(t,\lambda)$9 at $p_0$0, $p_0$1 at $p_0$2, and $p_0$3 at $p_0$4, with the merit function minimizing

$p_0$5

subject to constraints on beam deviation and throughput. The design keeps residual chromatic displacements within a $p_0$6 radius at the focal plane, while the pick-off mirror tilt prescription compensates the local chief-ray angle on the curved non-telecentric focal surface (Bestha et al., 2023).

Other implementations scale the same logic differently. HRMOS on the VLT is designed for high resolution, multi-object capability, and long-term stability in a $p_0$7–$p_0$8 field. The 2023 White Paper specifies $p_0$9–$\kappa_{\mathrm{cloud}}$0, multiplex $\kappa_{\mathrm{cloud}}$1–$\kappa_{\mathrm{cloud}}$2, and long-term stability $\kappa_{\mathrm{cloud}}$3, with science-driven access down to the blue optical. The 2026 concept paper gives a baseline resolving power $\kappa_{\mathrm{cloud}}$4 in three optical arms centered at $\kappa_{\mathrm{cloud}}$5, $\kappa_{\mathrm{cloud}}$6, and $\kappa_{\mathrm{cloud}}$7, approximate simultaneous windows of $\kappa_{\mathrm{cloud}}$8–$\kappa_{\mathrm{cloud}}$9, $P_{\mathrm{cloud}}$0–$P_{\mathrm{cloud}}$1, and $P_{\mathrm{cloud}}$2–$P_{\mathrm{cloud}}$3, and $P_{\mathrm{cloud}}$4–$P_{\mathrm{cloud}}$5 simultaneous targets over the full VLT Nasmyth $P_{\mathrm{cloud}}$6 field. Its dual-zone strategy uses a common field ADC in the central zone and a compact two-prism ADC per fiber in the peripheral zone, while each fiber module includes a double scrambler and a 19-slice image slicer. MSE adopts yet another scale: two identical high-resolution spectrographs produce $P_{\mathrm{cloud}}$7 simultaneous spectra, with Blue $P_{\mathrm{cloud}}$8–$P_{\mathrm{cloud}}$9 and Green $R_p/R_*$0–$R_p/R_*$1 at $R_p/R_*$2, Red $R_p/R_*$3–$R_p/R_*$4 at $R_p/R_*$5, and retunable working windows across $R_p/R_*$6–$R_p/R_*$7 by swapping dispersers and slightly adjusting camera focus and tilt (Magrini et al., 6 Jul 2026, Magrini et al., 2023, Zhang et al., 2018).

3. Observing strategy and reduction workflow

In the HRMOS exoplanet use case, fiber allocation within the $R_p/R_*$8–$R_p/R_*$9 field places one fiber on the transiting host star, $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$0–$d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$1 fibers on comparison stars of similar color and airmass, $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$2–$d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$3 sky fibers distributed across the field, and optionally fibers on activity standards. The recommended configurations prioritize simultaneous monitoring of Ca II H&K at $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$4, Na I D at $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$5, H$d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$6 at $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$7, K I at $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$8, the O I triplet at $d(\lambda)=\left(\frac{R_p(\lambda)}{R_*}\right)^2$9, and metal-line-rich regions such as $f/15$0–$f/15$1. Transit observations are described as time-critical and intensive, with typical durations $f/15$2 hours, a practical cadence of $f/15$3–$f/15$4 exposures, a pre-transit baseline of $f/15$5 hour, in-transit coverage of $f/15$6–$f/15$7 hours, and a post-transit baseline of $f/15$8 hour, with roughly $f/15$9–$2.18\ \mathrm{mm/arcsec}$0 in-transit and $2.18\ \mathrm{mm/arcsec}$1–$2.18\ \mathrm{mm/arcsec}$2 out-of-transit frames (Magrini et al., 2023).

A detailed reduction sequence is illustrated by the homogeneous HARPS/HARPS-N sodium survey. The analysis used archived pipeline s1d spectra that were background-subtracted, cosmic-ray corrected, flat-fielded, blaze corrected, and wavelength calibrated, rebinned to uniform $2.18\ \mathrm{mm/arcsec}$3 sampling and restricted to $2.18\ \mathrm{mm/arcsec}$4–$2.18\ \mathrm{mm/arcsec}$5. Telluric absorption was modeled and divided using molecfit v1.2.0 with $2.18\ \mathrm{mm/arcsec}$6–$2.18\ \mathrm{mm/arcsec}$7 isolated telluric line segments per night. When mesospheric Na emission was present and fiber B was set to sky, the fiber-B spectrum was subtracted from the stellar spectrum around the Na doublet. A master out-of-transit spectrum $2.18\ \mathrm{mm/arcsec}$8 was constructed as the weighted mean of fully out-of-transit spectra; residuals were then defined as

$2.18\ \mathrm{mm/arcsec}$9

The continuum of the residuals was normalized with a third-order polynomial, and a median filter of width $c(t,\lambda)$00 was applied at the end to remove broadband continuum residuals without affecting narrow lines. Residuals were shifted to the planetary rest frame using

$c(t,\lambda)$01

and CLV plus RM signatures were modeled on an $c(t,\lambda)$02 stellar grid with Kurucz ATLAS9 specific-intensity spectra across $c(t,\lambda)$03 values. Each residual was divided by the timestamp-matched RM/CLV model before combination. The final transmission spectrum was

$c(t,\lambda)$04

with inverse-variance weighting used throughout so that low-SNR pixels in deep stellar line cores do not bias the mean (Langeveld et al., 2022).

In the more general Mo-HRTS framework, the central ratioing step is

$c(t,\lambda)$05

where the weights $c(t,\lambda)$06 may be inverse-variance or learned by minimizing out-of-transit residuals. The high-resolution product is then

$c(t,\lambda)$07

while spectrophotometric light curves are obtained by binning

$c(t,\lambda)$08

A white-light curve is fit with a transit model in the PyLightcurve implementation of the Mandel and Agol formalism, and its residuals are used as a Common Mode Correction for the colored-light curves. In this sense, Mo-HRTS is not merely a hardware mode; it is an explicit joint reduction architecture linking line-resolved and broadband observables (Bestha et al., 23 Sep 2025).

4. Quantitative performance and retrieval leverage

The TMT/HROS study quantifies why Mo-HRTS is operationally difficult without field-aware chromatic control. In ZEMAX, the uncorrected atmosphere drives on-axis geometric radius from $c(t,\lambda)$09 ($c(t,\lambda)$10) to $c(t,\lambda)$11 ($c(t,\lambda)$12) at $c(t,\lambda)$13, far exceeding a $c(t,\lambda)$14 fiber diameter. Geometric throughput, defined as

$c(t,\lambda)$15

drops without ADC correction from $c(t,\lambda)$16 on-axis to $c(t,\lambda)$17 at $c(t,\lambda)$18, and off-axis from $c(t,\lambda)$19 to $c(t,\lambda)$20. With the per-object ADC at optimized $c(t,\lambda)$21, $c(t,\lambda)$22 is restored to $c(t,\lambda)$23 even at $c(t,\lambda)$24 across $c(t,\lambda)$25–$c(t,\lambda)$26. The design target is to maintain fiber coupling

$c(t,\lambda)$27

at $c(t,\lambda)$28 for a $c(t,\lambda)$29 fiber, while tolerancing with apex-angle $c(t,\lambda)$30, decenter $c(t,\lambda)$31, lens thickness $c(t,\lambda)$32, and tilt $c(t,\lambda)$33 gives average image-quality degradation $c(t,\lambda)$34. Rotational stage repeatability must hold $c(t,\lambda)$35 within $c(t,\lambda)$36 to preserve the $c(t,\lambda)$37 residual envelope (Bestha et al., 2023).

HRMOS frames the same question in survey terms. Its White Paper gives $c(t,\lambda)$38–$c(t,\lambda)$39, so that

$c(t,\lambda)$40

with $c(t,\lambda)$41 at $c(t,\lambda)$42 and $c(t,\lambda)$43 at $c(t,\lambda)$44. The ETC indicates SNR $c(t,\lambda)$45 in $c(t,\lambda)$46 hour for $c(t,\lambda)$47 and SNR $c(t,\lambda)$48 in $c(t,\lambda)$49 hour for $c(t,\lambda)$50. For a hot Jupiter, the atmospheric annulus signal per scale height is

$c(t,\lambda)$51

and for $c(t,\lambda)$52, $c(t,\lambda)$53, $c(t,\lambda)$54–$c(t,\lambda)$55, and $c(t,\lambda)$56–$c(t,\lambda)$57, the example gives $c(t,\lambda)$58 per scale height. For multi-line species, the detection scaling is summarized as

$c(t,\lambda)$59

so a $c(t,\lambda)$60-hour in-transit integration yields $c(t,\lambda)$61 for $c(t,\lambda)$62 and $c(t,\lambda)$63 for $c(t,\lambda)$64, with per-transit detections at the $c(t,\lambda)$65–several-$c(t,\lambda)$66 level for strong metal-line species when $c(t,\lambda)$67–$c(t,\lambda)$68 (Magrini et al., 2023).

The most direct demonstration of retrieval leverage appears in the UVES/FLAMES-like Mo-HRTS simulations for WASP-121 b. Those simulations used $c(t,\lambda)$69, SNR per resolution element of $c(t,\lambda)$70 for the target and $c(t,\lambda)$71 for the reference, one simultaneous G-type comparison star, and $c(t,\lambda)$72 orbital phases. After spectral division and phase alignment, the high-resolution transmission spectrum recovered Na D1 and D2 at the expected wavelengths, while $c(t,\lambda)$73 colored-light curves from the same dataset recovered a broadband transmission spectrum with a Rayleigh-like slope rising blueward to $c(t,\lambda)$74 and a pronounced sodium feature around $c(t,\lambda)$75. The proposed joint inference uses

$c(t,\lambda)$76

so that broadband information constrains $c(t,\lambda)$77, $c(t,\lambda)$78, and cloud parameters while the high-resolution component constrains resolved line cores, kinematics, and relative line depths. The paper emphasizes feasibility rather than a specific posterior-gain metric, but the methodological intent is explicit: Mo-HRTS is designed to mitigate HRTS-only normalization degeneracies with a single ground-based dataset (Bestha et al., 23 Sep 2025).

5. Exoplanet atmospheric applications and empirical population trends

The sodium survey of ten irradiated giant exoplanets provides the clearest empirical benchmark for what a homogeneous high-resolution transmission program can extract and therefore what Mo-HRTS could scale to larger samples. Weighted Gaussian fits to the D2 and D1 cores show one new Na detection in WASP-79b and confirm previous detections across the remainder of the sample. Seven planets have D2/D1 ratios consistent with unity within $c(t,\lambda)$79—HD 189733 b, WASP-21b, WASP-49b, WASP-79b, WASP-76b, MASCARA-2b, and KELT-9b—while WASP-69b, WASP-121b, and WASP-189b show D2 $c(t,\lambda)$80 D1 at $c(t,\lambda)$81. The same study measured consistent blueshifts of order $c(t,\lambda)$82–$c(t,\lambda)$83 across nine of ten planets, with WASP-79b inconclusive, and interpreted them as net day–night winds of a few $c(t,\lambda)$84. For relative Na atmospheric height, the analysis defines

$c(t,\lambda)$85

and fits the empirical relation

$c(t,\lambda)$86

with $c(t,\lambda)$87, $c(t,\lambda)$88, and $c(t,\lambda)$89, where $c(t,\lambda)$90. The interpretation given is that $c(t,\lambda)$91 decreases exponentially with $c(t,\lambda)$92 and saturates to $c(t,\lambda)$93 at large $c(t,\lambda)$94, providing a practical target-selection prior for future alkali surveys (Langeveld et al., 2022).

Mo-HRTS expands this single-target HRTS logic from sequential surveys to simultaneous differential observations. In the TMT/HROS concept, embedding an ADC in each positioner allows a transiting host and several comparison stars drawn from the $c(t,\lambda)$95 field to be observed simultaneously at $c(t,\lambda)$96, supporting common-mode telluric and instrumental systematics removal at high spectral resolution. The paper links this directly to exoplanet transmission spectroscopy, where the restored throughput from $c(t,\lambda)$97 to $c(t,\lambda)$98 at $c(t,\lambda)$99 is especially important in photon-starved blue-optical regimes and where per-object ADCs reduce chromatic aperture losses and color-dependent fiber effects that destabilize telluric division (Bestha et al., 2023).

HRMOS generalizes the exoplanet case to a multi-window, activity-aware mode. Its relevant optical windows include Ca II H&K in the blue, dense Fe-peak line regions in the green, and H$c(t,\lambda)$00 in the red. The 2026 paper identifies accessible line groups for Mo-HRTS in the baseline arms: Ca II H&K cores at $c(t,\lambda)$01, H$c(t,\lambda)$02 and H$c(t,\lambda)$03 in the blue, Mg I b at $c(t,\lambda)$04, $c(t,\lambda)$05, and $c(t,\lambda)$06 in the green, and H$c(t,\lambda)$07 at $c(t,\lambda)$08 in the red, together with Fe I/Fe II/Ti II/V/Cr forests favorable to cross-correlation. It also notes an important design limitation: the current baseline windows do not include the Na I D doublet at $c(t,\lambda)$09 or the K I doublet at $c(t,\lambda)$10, so alkali-focused programs would require complementary instruments or a future arm optimization (Magrini et al., 6 Jul 2026, Magrini et al., 2023).

6. Extensions to ultraviolet and ultra-high-resolution regimes, with limitations

The Mo-HRTS concept is not restricted to optical exoplanet spectroscopy. In the ultraviolet, the case for $c(t,\lambda)$11 over $c(t,\lambda)$12–$c(t,\lambda)$13 is motivated by sightline-based diagnostics of the baryon cycle and star–exoplanet interactions, including H I Ly$c(t,\lambda)$14 at $c(t,\lambda)$15, N V at $c(t,\lambda)$16, Si III at $c(t,\lambda)$17, O I at $c(t,\lambda)$18, $c(t,\lambda)$19, and $c(t,\lambda)$20, C II at $c(t,\lambda)$21, Si IV at $c(t,\lambda)$22, C IV at $c(t,\lambda)$23, Fe II multiplets near $c(t,\lambda)$24, and Mg II h&k at $c(t,\lambda)$25. The argument is sharpened by explicit degradation tests: in the $c(t,\lambda)$26 Cet Mg II example, three ISM components separated by $c(t,\lambda)$27 are cleanly separated at $c(t,\lambda)$28, whereas degrading to $c(t,\lambda)$29 misses a $c(t,\lambda)$30 component and yields column-density errors by a factor of $c(t,\lambda)$31, and degrading to $c(t,\lambda)$32 yields an error by a factor of $c(t,\lambda)$33. This suggests that UV Mo-HRTS would be valuable not only for exoplanet escape and stellar-activity monitoring but also for multiplexed ISM and CGM sightline programs in which simultaneous references or simultaneous multiple sightlines increase efficiency and help disentangle narrow, stationary interstellar components from time-variable signals (Linsky et al., 31 Mar 2025).

At even higher resolution, Fabry–Perot interferometer arrays and dualons have been proposed as front-end resolution boosters for Mo-HRTS biosignature work near the O$c(t,\lambda)$34 A-band. The laboratory 2-FPI prototype reached resolving power $c(t,\lambda)$35 at $c(t,\lambda)$36 with a single-mode fiber and a separate configuration reached $c(t,\lambda)$37 with improved tip–tilt alignment; a dualon chain reached $c(t,\lambda)$38 at the same wavelength. Predicted throughput from the Airy plus beam-deviation model is $c(t,\lambda)$39 for single-mode, $c(t,\lambda)$40 for a $c(t,\lambda)$41 fiber, and $c(t,\lambda)$42 for a $c(t,\lambda)$43 fiber, while the purity ratio is $c(t,\lambda)$44 for an etalon and $c(t,\lambda)$45 for a dualon at the $c(t,\lambda)$46 cut. The motivation is that current astronomical spectrographs typically achieve $c(t,\lambda)$47, whereas recent studies cited in that paper argue that $c(t,\lambda)$48–$c(t,\lambda)$49 is optimal for detecting O$c(t,\lambda)$50 in the atmosphere of Earth analogs with the ELTs; the same discussion states that boosting from $c(t,\lambda)$51 to $c(t,\lambda)$52–$c(t,\lambda)$53 can reduce the required number of transits by $c(t,\lambda)$54 (Rukdee et al., 2020).

Several limitations remain intrinsic to Mo-HRTS. The reference-star ratio provides a quasi-absolute continuum constraint, not true absolute calibration. Telluric and airmass cancellation by ratioing is effective but incomplete if target and reference stars differ in spectral type, and the present demonstration paper explicitly notes that CLV and RM were not included in its first simulation and must be modeled for precision work. Reference-star availability can be limiting, particularly for bright hot-Jupiter hosts in sparse fields. On the instrumental side, the TMT/HROS per-object ADC has been validated only over $c(t,\lambda)$55–$c(t,\lambda)$56 and over $c(t,\lambda)$57–$c(t,\lambda)$58; near $c(t,\lambda)$59 and at large zenith angles, model discrepancies can reach $c(t,\lambda)$60 if a simplistic atmospheric model is used. The HRMOS White Paper likewise notes trade studies among 4-Arms, Hybrid, and 1-Arm concepts, with the 4-Arms ADC near the focal plane described as challenging, and it identifies Mo-HRTS simulator development, PCA/SysRem-type pipelines, and Gaia-based pre-selection of reference stars as near-term requirements. These constraints do not negate the observing mode; they define the practical boundary conditions under which Mo-HRTS can preserve continuum information while retaining the spectral fidelity of high-resolution transmission spectroscopy (Bestha et al., 23 Sep 2025, Bestha et al., 2023, Magrini et al., 2023).