Rederivation of STIS Secondary Echelle Mode Traces

Imagine the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope as a giant, high-tech prism. When starlight hits it, the prism doesn't just show you a rainbow; it breaks the light into hundreds of tiny, parallel strips called "orders." Each strip is a different slice of the universe's spectrum, containing secrets about what stars are made of.

To read these secrets, astronomers need to know exactly where each strip of light lands on the telescope's digital camera (the detector). This path is called a "trace."

The Problem: The "Straight Line" Mistake

For the main, most popular settings of the telescope, the engineers knew that light doesn't travel in a perfectly straight line across the camera. It curves slightly, like a banana. So, they drew curved lines to follow the light perfectly.

However, for the "secondary" settings (specialized settings used to look at specific chemical lines in stars), the engineers took a shortcut. They assumed the light traveled in a perfectly straight line. They drew a straight ruler across the curved banana.

Why does this matter?
Imagine trying to catch a rolling ball in a net. If you hold the net straight but the ball is rolling in a curve, the ball will slip out the sides.

The Result: For years, when astronomers used these secondary settings, the telescope was accidentally "dropping" some of the starlight at the edges of the image. They were missing a few percent of the total light, which meant their measurements of how bright a star is were slightly off.

The Solution: The "Smart Rubber Band"

In this new report, the team (Siebert, Monroe, and Hernandez) decided to fix this. They didn't just draw a new straight line; they used a fancy mathematical tool called Gaussian Process Regression.

Think of this tool as a smart, stretchy rubber band.

The Old Way: You tried to force a straight stick to fit a curved path. It didn't work well at the ends.
The New Way: You take a flexible rubber band and gently stretch it over the actual path of the light. It naturally bends and curves exactly where the light bends, even if the curve is weird or wiggly.

This "smart rubber band" looks at the data point-by-point and figures out the smoothest, most accurate curve that fits the light, even in areas where the signal is a bit fuzzy or noisy.

The Results: Catching More Light

By switching from the "straight stick" to the "smart rubber band," the team found they could catch about 4% more light, especially near the edges of the camera where the curve is most pronounced.

Analogy: It's like realizing your fishing net had a hole in the corner. Once you patched it with the right material (the new curve), you suddenly caught 4% more fish without changing the bait or the boat.

What Changed?

The team went through the telescope's instruction manual (the reference files) and updated the maps for 9 different secondary settings.

Before: The map said, "Go straight."
After: The map says, "Follow the gentle curve."

They tested this on standard stars (celestial "rulers" used for calibration) and found that the new method works just as well as the best methods used for the primary settings. It's more accurate, it recovers lost light, and it ensures that when astronomers measure the brightness of a star, they aren't missing a piece of the puzzle.

In a Nutshell

The Hubble telescope was slightly "blind" at the edges of its specialized modes because it was using a straight ruler to measure a curved path. The scientists fixed the ruler by replacing it with a flexible, smart curve. Now, Hubble can see a little more of the universe, making our measurements of stars and galaxies more precise than ever before.

Here is a detailed technical summary of the Instrument Science Report STIS 2024-03, "Rederivation of STIS Secondary Echelle Mode Traces."

1. Problem Statement

The Space Telescope Imaging Spectrograph (STIS) utilizes four echelle gratings (E140H, E140M, E230H, E230M) to observe astronomical sources in the UV range. While "primary" observing modes have well-calibrated spectral traces that account for the curved paths of dispersed light across the detector, "secondary" modes (central wavelengths optimized for specific absorption/emission lines) have historically suffered from calibration limitations.

The Core Issue: Secondary mode traces were previously defined using straight-line fits to each spectral order.
The Consequence: Because echelle orders naturally exhibit curvature (especially near detector edges), straight-line traces fail to center the cross-dispersion profile correctly. This misalignment leads to flux loss, particularly at the edges of the detector, preventing the instrument from achieving its nominal flux accuracy (currently ~8% absolute, ~5% relative).
Context: Recent updates to standard star atmospheric models (CALSPECv11) have improved continuum accuracy, necessitating a corresponding update to the geometric extraction definitions (traces) to fully realize these gains.

2. Methodology

The authors developed a universal, automated method to redefine echelle traces using Gaussian Process (GP) regression, replacing the previous linear fitting approach. The workflow consists of three main stages:

A. Order Identification and Cross-Dispersion Fitting

Detection: Orders are identified by taking a median crosscut of the central 50 columns of the detector and applying a peak-finding algorithm (using scipy). A prominence threshold of 10% of the largest peak ensures all orders are detected.
Pixel-by-Pixel Profiling: For each identified order, the cross-dispersion profile is fitted pixel-by-pixel along the dispersion direction.
- A 3-pixel boxcar smoothing is applied to columns prior to fitting to mitigate undersampling issues.
- A Gaussian plus constant background is fitted to each column to determine the $Y$ -location of the trace.
- Quality Control: Fits with peak counts less than 5 $\times$ the background level are excluded. Uncertainties are scaled by a factor of 6 to reflect observed scatter.

B. Gaussian Process (GP) Modeling

Instead of spline fitting (which requires manual knot placement and struggles with varying length scales), the authors employ GP regression to smooth the noisy pixel-by-step measurements.

Kernel Selection: A Matern kernel (a generalization of the Radial Basis Function) is used with a smoothness parameter of 2.5 and an initial length scale of 10. This kernel was chosen because it offers greater flexibility in modeling the varying curvature of orders, particularly the "upturns" seen near detector edges.
Training: The model is trained on the measured profile centers. It estimates the kernel parameters to predict the trace location at every column of the detector.
Advantages:
- Handles low Signal-to-Noise (S/N) regions (e.g., strong absorption features or repeller wire shadows) by naturally interpolating/extrapolating rather than breaking.
- Provides an uncertainty estimate (95% confidence interval) for the trace.
- Automatically adapts to the specific curvature of each order without manual tuning.

C. Reference File Updates

The resulting traces are converted into offsets relative to the detector center and stored in the SPTRCTAB reference files (specifically modifying the A2DISPL keyword).

3. Key Contributions

New Trace Definition Algorithm: A robust, universal method using Gaussian Process regression that accounts for the detailed curvature of echelle orders, replacing the inadequate straight-line approximations for secondary modes.
Comprehensive Calibration: Application of this method to 9 specific secondary modes (covering E140H, E230H, and E230M gratings) for both pre- and post-Servicing Mission 4 (SM4) observations.
Flux Throughput Recovery: The new traces recover flux previously lost due to misalignment, directly improving the accuracy of the STIS flux calibration pipeline.

4. Results and Accuracies

The study quantified the improvements by comparing the new GP-derived traces against the old straight-line traces and primary mode traces.

Trace Accuracy:
- When applied to a primary mode (E230H/2263) as a test, the new method showed an average deviation of only 0.02 ± 0.02 pixels compared to existing primary traces, confirming the method's validity.
- Comparisons between different standard stars (G191-B2B vs. BD+284211) showed the method is insensitive to the specific calibrator star (average deviation ~0.05 pixels).
Flux Throughput Improvements:
- The new traces recover approximately 2–4% more flux, particularly near the detector edges where the curvature of the order is most pronounced.
- Specific gains by mode:
  - E230H/2713: 62% of orders saw >4% flux improvement.
  - E230M/2415: 55% of orders saw >4% flux improvement.
  - E140H/1271: 33% of orders saw >4% flux improvement.
Throughput Recalibration: The recovered flux translates to a 2–4% increase in derived throughput at the edges of the orders, aligning the sensitivity curves with the new standard star models.

5. Significance

This work is critical for the ongoing STIS flux recalibration effort. By correcting the geometric definition of the extraction regions, the instrument can now achieve its theoretical flux accuracy limits for secondary modes.

Immediate Impact: Updated reference files (SPTRCTAB) have been delivered for 9 frequently used secondary modes, benefiting both archival data re-reduction and future observations.
Future Utility: The Gaussian Process method provides a scalable framework. It can be applied to the remaining secondary modes without mode-specific tuning and could be extended in the future to 2D interpolation, utilizing high-S/N adjacent orders to inform the shapes of low-S/N orders.
Scientific Value: Improved flux accuracy is essential for precise abundance measurements, line profile analysis, and continuum studies in the UV spectrum, ensuring that STIS data remains competitive with modern spectroscopic standards.