Instrument drift check

Recap - Instrument drift and calibrators

MAROON-X wavelength and drift solution

MAROON-X is highly stabilized fiber-fed spectrograph and uses a temperature- and pressure-stabilized Fabry Perot etalon as its primary wavelength calibrator. The etalon provides a dense comb of unresolved emission lines that is ideal to trace the instrument drift of MAROON-X with high fidelity at a local level. The information density and 'purity' of the etalon greatly outperforms other sources of wavelength references, such as the ThAr HCL. Limited line density, high contrast between lines, and contamination from super-saturated Argon lines as well as from a floor of ThO2 molecular bands greatly limits the information density and precision of the ThAr spectrum. The etalon does allows to track the instrument drift with much higher fidelity.

To derive a wavelength solution and drift model from the etalon, an absolute wavelength reference is initially required to determine the thickness of the etalon spacer (which sets the spacing between etalon lines) and the chromatic dispersion of the etalon (which causes a deviation of the line positions from a regular grid in frequency space).

An initial wavelength solution is derived from Thorium lines only using a 2D Legendre polynomial in x (detector coordinate in dispersion direction) and m (echelle order number) of 8th degree in x and 6th degree in m, separately for each detector. Higher polynomial degrees do not improve the residuals of the fit. Based on this wavelength model, we can solve for the etalon spacer thickness and dispersion curve.

The general shape of the etalon dispersion is taken from a theoretical model of the mirror coating stack (credit to Julian). This dispersion model is then fitted with a spline whose knot number and positions are automatically determined to keep the residuals of the spline fit under 1m/s (Note: this is arbitrary in a way and not necessarily a good match to the uncertainties from the Thorium lines). This spline is then fit onto the measured etalon line positions on the initial wavelength solution. The theoretical dispersion model of the etalon and the nominal spacer thickness of 9.9984 mm are already good enough to identify the interference order number of each etalon peak to ~0.1, meaning there is no ambiguity or discontinuity of the etalon order numbers between echelle orders. After a re-fit of the spacer thickness and the spline model of the dispersion (keeping the spline knots at their previously determined 'optimum position' to match the expected shape of the dispersion curve), the spacer thickness and dispersion model are kept constant between observing runs. We thus treat the etalon as if it were perfect, but need to check if and how it drifts.

For each new observation a unique wavelength solution is derived from the etalon spectrum and the fixed etalon parameters using a cubic spline for each echelle order with 30 equidistant knots (Note: this is arbitrary again and was chosen to remove any systematic residuals in the wavelength solution as could be observed when using the 2D Legendre polynomial even of 26th degree in x and 23rd degree in m). Using the simultaneous calibration (aka simcal) fiber, we can determine the instrument drift between an etalon reference spectrum (with etalon lines both in the science fibers and the simcal fiber) and any other science spectrum taken reasonably close in time (typically within 6hrs or so). The differences in the etalon line positions in the simcal fiber are fitted in each order with a cubic spline using only 3 knots, to optimize the tradeoff between flexibility (i.e. allowing independent drifts and non-linear stretching of the instruments dispersion) and information content noise. The unique wavelength solution thus contains the instrument drift.

ThAr as a check of the etalon drift - Methods

As outlined above, we keep the etalon parameters that govern the positions (frequencies) of the etalon lines (i.e. spacer thickness and chromatic dispersion) constant over time due to the limited information content of any possibly 'absolute' reference source, like the ThAr spectrum. However, we know that the etalon itself is not perfectly stable but has potential for drifts too, most notably:

Achromatic linear drift from the shrinkage of the etalon spacer.
Achromatic drifts induced by temperature changes.
Chromatic drift from changes in the etalon mirror coatings.

The expected magnitude of the etalon drift is at the order of a few cm/s per day from the shrinkage of the etalon spacer. We can now try to use the limited information from the ThAr spectrum to track the etalon behavior over time, hoping that drifts will be linear enough that we can use ThAr observations collected over long time scales (months) to back out the low-level drifts of the etalon. Due to the limited information content of the ThAr spectrum, useful measurements can only be derived on a per-order basis by done using one of two different implementations of the cross-correlation technique, namely either (I) against a binary line list or (II) by cross-correlating each spectrum against an empirical reference spectrum, e.g. the spectrum used for the determination of the etalon parameters. Each of these two approaches can in turn be executed on either (a) a static wavelength solution or (b) on the drift-corrected wavelength solution.

Method (a) is easier to implement and has the advantage that there is no uncertainty from determining the drift solution for the ThAr frame from the etalon data. The result is the absolute drift of the spectrograph. The difference between the drift solution for the spectrograph based on the etalon data with the one from the ThAr data could then be assigned to drifts of the etalon. The disadvantage of this approach is that spectrograph dispersion changes over time coupled with the different local distribution of RV information in each order cause a large spread of RV drifts from order to order. This limitation makes this approach useless as uncertainties for the drift easily reach 1 m/s.

Method (b) is harder to implement but limits the influence of the non-homogenous distribution of the RV information in the ThAr spectrum since the wavelength-dependance of the expected etalon drifts is small across an echelle order. Practically, the instrument drift correction of the ThAr frames can be achieved either from bracketing etalon observations or by using the simcal fiber as in the case of science exposures. The difficulty is to correct for the bleeds of the Ar lines into the etalon spectrum. However, since instrument drifts can reach values of up to 1 m/s from exposure to exposure, and are sometimes non-linear to a degree that limits the precision when using the bracketing etalon technique, we implemented simultaneous etalon observations starting in August 2021.

(I) Absolute cross-correlation against a line list

When cross-correlating the spectrum against line positions from the NIST line list for Thorium, we recover the intrinsic average instrumental profile (IP) in each echelle order since the Th lines are unresolved. MAROON-X' IP is not very well described by a Gaussian profile, but much better by a box (representing the square slit) and error functions on either side (representing the aberrations of the spectrograph). This IP is used when fitting the (unresolved) etalon lines in the etalon spectrum and matches very well. When the sigmas of the two error functions are tied together, the fit is symmetrical, if left as a free parameter, the fit allows for asymmetric IPs which is more realistic but has its downsides (see discussion below).

The main advantages of the 'absolute' cross-correlation against the NIST line list are (1) the ability to select only Thorium lines which are regarded the most stable, and discarding the Argon and ThO2 lines which might show a stronger variability (e.g. changes in temperature of the lamp, i.e. 'on'-time) and might be more prone to lamp aging effects; and (2) the ability to easily avoid regions of contamination from saturated Argon lines, particularly in the red arm.

The main disadvantages are (1) sparse and uneven sampling across each order due to the limited number of Thorium lines and (2) contamination issues arising from line blends, and the floor of ThO2 lines across the spectrum.

(II) Relative cross-correlation against an empirical template spectrum

When cross-correlating the spectrum against an empirical ThAr spectrum, the cross-correlation profile is Gaussian for each echelle order. The main advantages of this 'relative' cross-correlation are (1) maximization of the information content as it uses all of the spectral content, including the dense forrest of ThO2 lines, and (2) independence of errors or uncertainties in spectral line lists. The disadvantages are (1) a broader cross-correlation profile from correlating two resolved spectra, (2) potentially reduced stability of the ThAr spectrum from including Ar and ThO2 lines that might have inferior time stability, (3) the inability to select or weight content short of masking certain spectral regions, (4) unresolved ThO2 bandheads and extended wings of severely overexposed Ar lines changing the shape of the cross-correlation function. Particularly in the red arm we find the high number of line bleeds to pose a challenge for the practical implication of the cross-correlation as masking regions is not straightforward in a dense emission spectrum.

ThAr as a check of the etalon drift - Implementation

(1) Retrieval and filtering for Thorium line list

The first step is the retrieval and filtering of the Thorium line list from the NIST website. The script analyze/recipes/query_NIST_ThAr.py downloads the NIST data, reformats them as numpy arrays and saves them as NIST_ThAr_numpydata.nz.

Down-selecting the Th lines based on line strengths and blends is handled in function condition_NISTcatalog() in analyze/recipes/xcorr_ThAr_NIST_and_relative.py. This function receives a measured ThAr spectrum and a flat together with a saturation limit (1D counts) and a low-SNR cutoff (also as 1D counts). It then removes weak and saturated lines from the catalog based on the values found in the measured spectrum. Blended lines (catalog lines with <5km/s separation) are removed from the catalog as well. It then proceeds to a cross-correlation (see below) of the remaining lines against the measured spectrum on a line-by-line basis and further rejects catalog lines that don't match a number of fit criteria (e.g. rejected/unsuccessful fits, widths larger than typical line profiles (indicating unresolved line blends), or deviations from the expected position of more than 300 m/s. The result of this procedure is a down-selected Th line list as well as a saturation mask for each order (marking regions to be excluded from future fits).

The get_NISTcatalog() function is called when the high-level data processing function NISTxcorr_to_hd5store() is called with the keyword conditionNIST set to True. The line list and saturation mask are then also stored in a pandas hd5 file. This file is read in when conditionNIST is set to False, which should be the default setting.

Note: Changing the content of either the line list or of the saturation mask will have an impact on the measured RVs. The conditioning of the NIST line list should thus only be done once and only measurements using the same line list and saturation mask should be compared.

(2) Pre-processing of the ThAr frames

ThAr raw spectra can be flux extracted just like science spectra, see Flux Extraction. No dark subtraction is necessary for DTTTD, and DTTTT, and spectra. For DTTTE spectra, a DTTTD dark should be applied only to fiber 5 (hence, set skip dark = 2-4) to remove bleeding Ar lines from the etalon spectrum in the simcal fiber.
DTTTD, and DTTTT frames need to receive their wavelength vector from an adjacent etalon frame, either as a direct copy or by interpolating between bracketing etalons. Use routine analyze/recipes/batch_ThAr_wls.py for this task. Make sure the etalon frames are fully processed (flux extracted, etalon lines fitted and spline solution determined).
DTTTE frames need to be processed for Etalon Line Fitting first before moving on to wavelength calibration. Due to the contamination from the ThAr spectrum, the etalon fitting should be done using a reference DEEEE file via . After the line fitting is complete, the DTTTE frames can be processed like a regular science frame to have a wavelength and drift solution applied, see Drift Solution.

(3) Cross-correlation processing of the ThAr frames

Cross-correlation and subsequent plotting is handled by analyze/recipes/xcorr_ThAr_NIST_and_relative.py using a two step procedure.
In step one, a set of ThAr files are analyzed via cross-correlation, either against the NIST line list (i.e. 'absolute') or against a ThAr reference spectrum (i.e. 'relative'). Both methods are discussed below. The output of step one are pdf files for each ThAr frame showing the spectra and cross-correlation results as well as a per-fiber summary on the last page. The results are written into a pandas hd5 file.
In step two, the measurements are loaded from the hd5 file, analyzed and plotted.

(3.1) Cross-correlation against the NIST Th line list

Cross-correlation against the NIST Th line list is handled by function NISTxcorr_to_hd5store() in analyze/recipes/xcorr_ThAr_NIST_and_relative.py . Input parameters are a list of pre-processed ThAr frames, a master flat (for determining the blaze function), and the name of the output hd5 file holding the results of the order-by-order cross-correlation over the input files. If the NIST line list has been downloaded and properly conditioned (see point 1 above), conditionNIST should be set as False and the name of the NIST line list given as the NIST_file parameter in the call.
Cross-correlation processing, fitting of the cross-correlation function, and plotting are done in function get_binary_xcor_data(). The actual cross-correlation is handled in function binary_crosscorrelation(). It uses a hardwired lag (-5000 to 5000 m/s in 50m/s steps) and uses scipy.interpolate.interpol1D() to sample the spectrum at the various lag points with linear interpolation. The spectrum is properly de-blazed. The cross-correlation function is fitted with a linear + IP composite model using lmfit. The instrumental profile (IP) is modeled using the peak() function developed for the etalon line fit. The model is the sum of two err functions which approximate the convolution of a rectangle step function of a certain amplitude and width (representing the slit image), with two gaussians (each with certain amplitude and sigma). The resulting model has a center, an amplitude, a half-width and two sigma values. We enforce a symmetric line fit by tying the sigma values together. We do further not enforce the line shape to match the IP as retrieved from the etalon fit.

(3.1) Cross-correlation against an empirical reference ThAr spectrum

Cross-correlation against an empirical reference ThAr spectrum handled by function xcorr_to_hd5store() in analyze/recipes/xcorr_ThAr_NIST_and_relative.py Input parameters are a list of pre-pre-processed ThAr frames, a master flat (for determining the blaze function), the name of the output hd5 file holding the results of the order-by-order cross-correlation over the input files, the reference file with a ThAr spectrum against which to perform the cross-correlations, a saturation cut-off value and diff_limit, a cut-off value to find steep flux gradients indicative of blooming (bleeding of super-saturated lines into adjacent orders).
Cross-correlation processing, fitting of the cross-correlation function, and plotting are done in function get_xcor_data(). Spectra are analyzed order-by-order and a saturation mask for each order is built from the reference spectrum and the provided saturation cutoff value. A fixed half-width of 10 pixel is used around saturated pixels to remove the line wings. A hard-coded list of Argon line positions in each order of the red arm is used to mask those lines as well. In addition, line bleeds are detected by looking for sharp drops in the flux level (bleeds have no wings in dispersion direction) exceeding the diff_limit parameter and masked as well. Each order is resampled via linear interpolation onto an oversampled logarithmic wavelength axis (default oversampling factor: 5). The RV step per log(wavelength)-axis pixel is now constant for each order (MSPP - meter per second per pixel). A constant lag of +/-7km/s is used for the cross-correlation, which is delivered by the crosscorrelation() function with similar output as numpy.correlate().
The spectra are de-blazed before cross-correlating, which is necessary to correct for skews in the lines from the blaze but likely deteriorates the SNR. the cross-correaltion profile is fitted with a linear + gaussian composite model using lmfit.

(4) Analysis and visualization of cross-correlation results.

The xcorr_to_hd5store() and NISTxcorr_to_hd5store() functions in analyze/recipes/xcorr_ThAr_NIST_and_relative.py produce pandas hd5 files for each set of input spectra. The hd5 files contain the results of the fits to the cross-correlation on an order-by-order basis for each fiber in each input frame. Analysis and visualization of the data is handled by function plot_science() in analyze/recipes/xcorr_ThAr_NIST_and_relative.py . This function takes the pandas data frame (or a list of data frames) read from the hd5 file(s) using function hd5store_to_pd() and a number of optional keywords. The processing follows these steps:

(4.1) Determine begin and end date/time if multiple runs are present

The input to plot_science() can be either a single pandas data frame or a list of data frames. The user can choose to either combine those data into a single 'run' or, by setting keyword find_runs to True the automatically find gaps larger than 7 days in the data, determine the respective begin and end datetimes, and group the data into separate runs. This will later allow to combine data to optimize information content and analyze the data for long-term changes, e.g. chromatic drifts.

(4.2) Remove unwanted echelle orders and outliers

Echelle orders that are known to perform worse than others, for example by having a larger variability or less RV content, can be completely removed from the subsequent analysis steps by specifying them as a list for argument ignore_orders of function plot_science(). In addition, statistical outlier removal is implemented on both a per-order basis (against the order-mean of a single frame) and on a per-observation basis (if more than 10 orders are marked as outliers) in any given frame. The clipping is based on a kappa-sigma approach, were the expected rms (the median of the standard deviation of all fibers with ThAr signal in a given frame) is scaled by a factor sigma_clip, provided as an argument to function plot_science() and data exceeding this limit are removed. If the same echelle orders are often removed as outliers for a number of frames in a run, adding this order to the ignore_orders list should be considered to avoid skewing results.

(4.3) Remove fixed offset pattern

Empirically we find that for both absolute and relative cross-correlation measurements, each order appears to have a fixed RV offset in respect to the mean of all orders. This is more pronounced when performing the cross-correlation on a time-invariant wavelength grid, i.e. when ignoring the drift of the spectrograph, but at the m/s level is also present when processing spectra on a drift-corrected wavelength grid. For each run the order mean is subtracted from all data and the time-averaged difference of the RV of each order to the global mean is determined and this static pattern is subtracted from the data. The order mean is then added back to the data to preserve any temporal variability of the mean over time. The static pattern is also only computed from the first run to preserve changes in the fixed offset pattern over time (which could be indicative of chromatic changes in the etalon). This step reduces the uncertainty in the order-mean RV by tightening the distribution of RVs from the orders.

(4.4) Perform statistics on the cross-correlation results

The code calculates the kapp-sigma clipped (kappa=4) weighted mean and the weighted error of the mean over all orders for:

(4.4.1) each fiber in each frame (order-mean),

(4.4.2) data grouped into one hour long 'observations', In this step the code also computes the residuals of the order mean from the observation mean for each frame.

(4.4.3) data grouped into runs as determined in step 4.1.

Both observation mean (4.4.2) and run mean (4.4.3) allow the correction of any offsets between the individual fibers if the keyword correct_longtermmean is set True when calling plot_science() . This is useful when calculating statistics and fibers show offsets as we assume that the etalon spectrum should behave identically in all three fibers and changes between fibers are due to the spectrograph, not the etalon.

The code calculates linear fits to the per-observation mean of all observations and of observations within a run.

(4.5) Auxiliary data

The code can receive a pandas data frame (or list of data frames) with ThAr lamp power on times retrieved via the InfluxQuery() class from the Netbooter entry in the influxDB database of the instrument. When given, the code calculates the time elapsed between lamp power on and any given frame and correlates this against the deviation of the RV order mean of each frame from a linear fit.

Additionally, the code will use flux information (the mean flux in each order and fiber) when stored during processing of the ThAr frames. Like with the lamp on times, the code will plot the correlation of the flux difference between the template and each observation and the deviation of the RV order mean of each frame from a linear fit.

(4.6) Plots & Output

Figure 1 - Drift rates between runs: Comparison of the overall drift rate (m/s/day) to the inter-run drift rate (difference between mean drift in each run divided by time difference). The difference in drift rate for each order between runs is plotted as well.

Figure 2 - Fixed order offset (and its change) determined per run: The fixed offset pattern between orders (see 4.3) is plotted for each run as well as the difference between runs to evaluate chromatic changes in the drift.

Figure 3 - Absolute FWHM (and its change) determined per run: The FWHM of the fit to the cross-correlation profile is plotted for each run as well as the difference between runs to evaluate whether intrinsic changes in the spectrograph IP might influence the measurements.

Figure 4 - Drift plot for all data, time elapsed between lamp being turned on and data taken, flux difference between template spectrum and individual frame and correlations between these quantities.

Figure 5 (interactive) - Drift plot for all data, including linear slope fits and residuals to either the observation mean or the linear slope.

Output:

Linear trend in per-observation mean over all runs
Intra-run slope for each run
Weighted average of drift-rates of all orders between pairs of runs

ThAr as a check of the etalon drift - Results 2021B - relative x-corr, blue arm

Starting in August 2021, ThAr frames were taken like science frames, i.e. with simultaneous etalon calibration light in fiber 5. Observations were typically taken three times a night when the frontend was on the telescope.

(1) Relative measurements, Blue arm

The per-fiber uncertainty in observation mean is 0.2 m/s along the whole sequence when cross-correlated against the first frame (2021-08-10T2132) except for the outliers, discussed below). This is a marked improvement over data taken in earlier semesters, were wavelength and instrument drift correction was done with bracketing etalon frames only.
The data show a linear trend with -2.0 +/- 0.1 cm/s/day (note the sign reversal due to the order of the cross-correlation, the actual drift in the data is positive). The August run matches the overall trend to within the uncertainty, but the November run has reduced intra-run trend of only -0.7 cm/s/day.
There are a number of outliers, particularly in the second run of the semester. They fall into two categories:
1. RV residuals to the linear trend show a strong correlation with the elapsed time after powering on the ThAr lamp. We can model this very nicely with a exponential function sigma_RV = (a - b*(exp(x/c), where x is the elapsed time and sigma_RV is the residual to the linear trend. Best fit values are a = 3.80, b = 0.3345, c = -5.786.
  In general, data taken 'too early', i.e. before the lamp has settled show a lower RV and have less flux than the reference spectrum. They also exhibit larger RV uncertainties as the individual orders show a larger spread of cross-correlations values.
2. A few data points that present as outliers exhibit a different characteristic. They show large flux excess compared to the reference spectrum (up to almost 100%) and they are outliers on the exponential law between residuals and elapsed time after lamp switch on. Further investigation shows that the exposure meter flux recorded for those frame show long cyclic deviations instead of the normal constant flux. The flux variations in the exposure meter are much smaller than the ones recorded in the spectrum itself, which seems to indicate that the exposure meter is dominated by the bright Argon lines (which are saturated in the spectra), not by the Thorium lines. This effect was most prominent on 2021-11-04T02:32-02:35, 2021-11-06T02:28-2:35 and 2021-11-7T02:50-02:54. It appears that the lamp is undergoing some periods of instability from time to time. The effect in the RVs is however less pronounced as the settling effect after power turn on.
After removal of the outliers, the residuals to the linear trend improve from rms= 0.30 m/s to 0.15 m/s for the August run and rms = 0.83 m/s to 0.18 m/s for the November run.
While there is no significant change in the static order offset pattern or the FWHM of the x-correlation function between the two runs, the slope of the linear trend, when fitted separately for each order shows a notable scatter, which might be statistically significant.

ThAr as a check of the etalon drift - Results 2021B - relative x-corr, red arm

(1) Relative measurements, red arm

The per-fiber uncertainty in observation mean is 0.3 m/s along the whole sequence when cross-correlated against the first frame (2021-08-10T2132) except for the outliers, discussed below). This is a marked improvement over data taken in earlier semesters, were wavelength and instrument drift correction was done with bracketing etalon frames only.
The data show a linear trend with -2.6 +/- 0.1 cm/s/day (note the sign reversal due to the order of the cross-correlation, the actual drift in the data is positive). The August run alone has a has much reduced trend of -0.2 cm/s/day while the November run fits the overall slope within the errors (basically the opposite behavior of the blue arm).
There are a number of outliers, particularly in the second run of the semester. They fall into two categories:
1. RV residuals to the linear trend show a strong correlation with the elapsed time after powering on the ThAr lamp. The correlation looks slightly different from the blue arm with a more linear trend at the beginning, but the exponential function used for the blue arm still works well. Best fit values are a = 1.82, b = 0.165, c = -4.56.
  In general, data taken 'too early', i.e. before the lamp has settled show a lower RV and have less flux than the reference spectrum. They also exhibit larger RV uncertainties as the individual orders show a larger spread of cross-correlations values.
2. A few data points that present as outliers exhibit a different characteristic. They show large flux excess compared to the reference spectrum (up to almost 100%) and they are outliers on the exponential law between residuals and elapsed time after lamp switch on. Further investigation shows that the exposure meter flux recorded for those frame show long cyclic deviations instead of the normal constant flux. The flux variations in the exposure meter are much smaller than the ones recorded in the spectrum itself, which seems to indicate that the exposure meter is dominated by the bright Argon lines (which are saturated in the spectra), not by the Thorium lines. This effect was most prominent on 2021-11-04T02:32-02:35, 2021-11-06T02:28-2:35 and 2021-11-7T02:50-02:54. It appears that the lamp is undergoing some periods of instability from time to time. The effect in the RVs is however less pronounced as the settling effect after power turn on.
After removal of the outliers, the residuals to the linear trend remain constant at rms= 0.22 m/s for the August run and improve from rms = 0.47 m/s to 0.21 m/s for the November run.
There is some indication of changes in the static order offset pattern or the FWHM of the x-correlation function between the two runs. The slope of the linear trend, when fitted separately for each order shows a much larger scatter than the blue arm.

ThAr as a check of the etalon drift - Results 2021B - absolute x-corr, blue arm

(1) Absolute measurements, blue arm

The per-fiber uncertainty in observation mean is 0.2 m/s along the whole sequence when cross-correlated against the conditioned NIST list. A few outliers show larger uncertainty of 0.4 m/s on average. This is a marked improvement over data taken in earlier semesters, were wavelength and instrument drift correction was done with bracketing etalon frames only.
The data show a linear trend with +2.0 +/- 0.1 cm/s/day (note the sign reversal compared to the relative measurements due to the order of the cross-correlation, the actual drift in the data is indeed positive). The August run alone has a has a slightly reduced trend of 1.4 cm/s/day while the November run matches the overall drift.
Unlike for the relative x-correlation, the outliers from lamp-on time effects are are indistinguishable from the noise. Outliers due to intrinsic lamp flux variations (see discussion in the relative x-correlation section) are are less pronounced but dominate the outlier budget.
No outlier removal has been attempted and the residuals to the linear trend are rms= 0.12 m/s for both the August and November runs.
There is some indication of changes in the static order offset pattern but the half-width and sigma values of the x-correlation function between the two runs remain the same. The slope of the linear trend, when fitted separately for each order shows a notable scatter.

ThAr as a check of the etalon drift - Results 2021B - absolute x-corr, red arm

(1) Absolute measurements, red arm

The per-fiber uncertainty in observation mean is 0.2 m/s along the whole sequence when cross-correlated against the conditioned NIST list. A few outliers show larger uncertainty of 0.4 m/s on average. This is a marked improvement over data taken in earlier semesters, were wavelength and instrument drift correction was done with bracketing etalon frames only.
The data show a linear trend with +2.6 +/- 0.1 cm/s/day (note the sign reversal compared to the relative measurements due to the order of the cross-correlation, the actual drift in the data is indeed positive). The August run alone has a has much reduced trend of 0.6 cm/s/day while the November run shows a slightly larger drift of + 3 .0 cm/s/day.
The outliers are due to the same sources as discussed in for the relative x-correlations. They fall into two categories:
1. RV residuals to the linear trend show a strong correlation with the elapsed time after powering on the ThAr lamp. The correlation resembles the one found for the relative x-correlation of the blue arm. Applying the same model, the best fit values are a = -0.735, b = -0.084, c = -4.97. The magnitude of the effect is about the same time constant but a much smaller amplitude (by a factor of 5 or so). Like for the relative x-correlation, the affected data exhibit larger RV uncertainties as the individual orders show a larger spread of cross-correlations values.
2. Outliers due to intrinsic lamp flux variations. See discussion in the relative x-correlation section. While these outliers are present here as well, they are less pronounced but dominate the outlier budget when correcting for the lamp-on time effect.
After removal of the outliers, the residuals to the linear trend remain constant at rms= 0.22 m/s for the August run and improve from rms = 0.27 m/s to 0.20 m/s for the November run.
There is some indication of changes in the static order offset pattern but the half-width and sigma values of the x-correlation function between the two runs remain the same. The slope of the linear trend, when fitted separately for each order shows a notable scatter which is also larger than the scatter in the blue arm.

ThAr as a check of the etalon drift - Results 2021A - relative x-corr, blue arm

ThAr frames were taken with ThAr in all science fibers and the simcal fiber. Bracketing etalon frames were taken for instrument drift correction and the wavelength and drift solution was interpolated between the nearest etalon frames taken before and after the ThAr frame.

(1) Relative measurements, blue arm

The per-fiber uncertainty in observation mean is 0.2-0.3 m/s for the first run in February, 0.2-0.5 m/s for the second and third run in April and May when cross-correlated against the first frame (2021-02-17T2226).
The data show a linear trend with -1.7 cm/s/day (note the sign reversal due to the order of the cross-correlation, the actual drift in the data is positive). The intra-run trends are -6.2, -5.0 and +2.0 cm/s/day. The trend between the 1st and 2nd run is -1.5 +/- 0.3 cm/s, while the trend between the 2nd and 3rd run is -2.9 +/- 0.3 cm/s/day.
When excluding the bluest orders (121 - 124), the overall slope is -2.2 cm/s/day with inter-run trends of -5.6, -3.3, and -1.0 cm/s. The trend between the 1st and 2nd run is -2.0 +/- 0.1 cm/s, while the trend between the 2nd and 3rd run is -3.0 +/- 0.3 cm/s/day.
A lamp-on effect is not present in the data and no outlier removal has been attempted. The residuals to the linear trend are rms ~ 0.6 m/s for all three runs.
There is a clear indication of changes in the static order offset pattern between the 2nd and 3rd run, as well as a notable shift in the FWHM values of the x-correlation function between these two runs. The slope of the linear trend, when fitted separately for each order, shows a strong scatter, particularly for all orders between the 2nd and 3rd run. Fibers 4 and 5 also have a strong difference in drift behavior for runs 2 and 3. We clearly see a change in the spectrograph IP between runs 2 and 3.

ThAr as a check of the etalon drift - Results 2021A - relative x-corr, red arm

(1) Relative measurements, red arm

The per-fiber uncertainty in observation mean is 0.2-0.6 m/s for the first run in February, 0.3-0.8 m/s for the second run in April and 0.5-1.0 m/s for the 3rd run in May. when cross-correlated against the first frame (2021-02-17T2226).
The data show a linear trend with -4 cm/s/day (note the sign reversal due to the order of the cross-correlation, the actual drift in the data is positive). The intra-run trends are +4.4, -3.3 and -6.4 cm/s/day. The trend between the 1st and 2nd run is -2.6 +/- 0.2 cm/s, while the trend between the 2nd and 3rd run is -6.4 +/- 1.3 cm/s/day.
A lamp-on effect is not present in the data and no outlier removal has been attempted. The residuals to the linear trend are rms ~ 2.0 m/s for all three runs.
There is a strong indication of changes in the static order offset pattern between the 2nd and 3rd run, as well as a strong shift in the sigma sigma values of the x-correlation function these two runs. The slope of the linear trend, when fitted separately for each order, shows a strong scatter, particularly for all orders between the 2nd and 3rd run. Fibers 4 and 5 also have a strong difference in drift behavior for runs 2 and 3. We clearly see a change in the spectrograph IP between runs 2 and 3.

ThAr as a check of the etalon drift - Results 2021A - absolute x-corr, blue arm

(1) Absolute measurements, blue arm

The per-fiber uncertainty in observation mean is 0.2 m/s for the February run and 0.3 m/s for April and May runs. No clear outlier are present among the scatter.
The data show a linear trend with +2.7 cm/s/day but the runs show clear deviations from this mean. (note the sign reversal compared to the relative measurements due to the order of the cross-correlation, the actual drift in the data is indeed positive). The intra-run slopes are 4.6, 0.9 and 1.2 cm/s/day for the three runs respectively. The trend between the first two runs is 1.8 cm/s/day, the trend between the second and third run is 4.5 cm/s/day.
A lamp-on effect is not present in the data. and no outlier removal has been attempted. The residuals to the linear trend are rms ~ 0.44 m/s for all three runs.
There is some indication of changes in the static order offset pattern and a strong shift in the sigma sigma values of the x-correlation function between the 2nd and 3rd run. The slope of the linear trend, when fitted separately for each order, shows a strong scatter. This is particularly notable for the bluest orders (125 - 122) for the first and second run and for all orders between the 2nd and 3rd run. Fibers 4 and 5 also have a strong difference in drift behavior for runs 2 and 3. We clearly see a change in the spectrograph IP between runs 2 and 3.

ThAr as a check of the etalon drift - Results 2021A - absolute x-corr, red arm

(1) Absolute measurements, red arm

The per-fiber uncertainty in observation mean is 0.2-0.6 m/s for the February and April run and 1.1-1.6 m/s for the May run, indicating a strong change in the static offset pattern for the May run. No clear outlier are present among the scatter.
The data show a linear trend with +6.2 cm/s/day but the runs show clear deviations from this mean. (Note the sign reversal compared to the relative measurements due to the order of the cross-correlation, the actual drift in the data is indeed positive). The intra-run slopes are 0.8, 3.3 and 6.6 cm/s/day for the three runs respectively. The trend between the first two runs is 3.1 cm/s/day, the trend between the second and third run is 10.7 cm/s/day.
A lamp-on effect is not present in the data. and no outlier removal has been attempted. The residuals to the linear trend are rms ~ 1.8 m/s for all three runs.
There is a strong indication of changes in the static order offset pattern between the 2nd and 3rd run, as well as a strong shift in the sigma sigma values of the x-correlation function these two runs. The slope of the linear trend, when fitted separately for each order, shows a strong scatter, particularly for all orders between the 2nd and 3rd run. Fibers 4 and 5 also have a strong difference in drift behavior for runs 2 and 3. We clearly see a change in the spectrograph IP between runs 2 and 3.

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