# Contamination in TESS light curves: The case of the Fast Yellow Pulsating
Supergiants

May G. Pedersen Sydney Institute for Astronomy, School of Physics, University
of Sydney NSW 2006, Australia  Kavli Institute for Theoretical Physics, Kohn
Hall, University of California, Santa Barbara, CA 93106, USA  Keaton J. Bell
Department of Physics, Queens College, City University of New York, Flushing,
NY-11367, USA

###### Abstract

Given its large plate scale of 21″ pixel-1, analyses of data from the TESS
space telescope must be wary of source confusion from blended light curves,
which creates the potential to attribute observed photometric variability to
the wrong astrophysical source. We explore the impact of light curve
contamination on the detection of fast yellow pulsating supergiant (FYPS)
stars as a case study to demonstrate the importance of confirming the source
of detected signals in the TESS pixel data. While some of the FYPS signals
have already been attributed to contamination from nearby eclipsing binaries,
others are suggested to be intrinsic to the supergiant stars. In this work, we
carry out a detailed analysis of the TESS pixel data to fit the source
locations of the dominant signals reported for 17 FYPS stars with the Python
package TESS_localize. We are able to reproduce the detections of these
signals for 14 of these sources, obtaining consistent source locations for
four. Three of these originate from contaminants, while the signal reported
for BZ Tuc is likely a spurious frequency introduced to the light curve of
this 127-day Cepheid by the data processing pipeline. Other signals are not
significant enough to be localized with our methods, or have long periods that
are difficult to analyze given other TESS systematics. Since no localizable
signals hold up as intrinsic pulsation frequencies of the supergiant targets,
we argue that unambiguous detection of pulsational variability should be
obtained before FYPS are considered a new class of pulsator.

CCD photometry (208) — Time series analysis (1916) — Light curves (918) —
Light curve classification (1954) — Variable stars (1761) — Photometry (1234)

††facilities: TESS (Ricker et al., 2014), Gaia (Gaia Collaboration et al.,
2016, 2022; Babusiaux et al., 2022)††software: astropy (Astropy Collaboration
et al., 2013, 2018), TESS_localize (Higgins & Bell, 2023), lightkurve
(Lightkurve Collaboration et al., 2018), astroquery (Ginsburg et al., 2019),
tesscut (Brasseur et al., 2019), numpy (Harris et al., 2020), matplotlib
(Hunter, 2007), pandas (pandas development team, 2020; Wes McKinney, 2010),
MESA (Paxton et al., 2011, 2013, 2015, 2018, 2019; Jermyn et al., 2022).

##  1 Introduction

The Transiting Exoplanet Survey Satellite (TESS Ricker et al., 2014) is
obtaining extensive time series photometry over most of the sky, enabling the
study of photometric variability of nearly all types of astronomical objects.
Interested in the behavior of massive evolved stars, Dorn-Wallenstein et al.
(2019, hereafter DW19) inspected TESS light curves for variability that could
improve our understanding of these objects. In addition to apparent luminous
blue variables (LBVs), unprecedented variability was identified in the TESS
light curves of three yellow supergiants (YSGs). The most notable of these is
HD 269953, which shows multiple periodicities.

That work was later extended, utilizing the full TESS Cycle 1 dataset to
investigate variability of 76 YSGs (Dorn-Wallenstein et al., 2020, hereafter
DW20). Among these, a total of five (HD 269953, HD 269110, HD 268687, HD
269840, and HD 269902) were interpreted to be rapidly pulsating on $\sim$day
timescales, suggesting that these belong to a new class of pulsator, which
were named FYPS for “fast yellow pulsating supergiants.” If this is true, then
FYPS would offer new exciting opportunities for studying and modelling the
interiors of evolved massive stars.

Figure 1: Position of the 17 FYPS stars in the HR diagram (top) and their
dominant frequency $f_{0}$ reported by DW22 as a function of effective
temperature (bottom). Blue circles indicate LMC stars, whereas orange
triangles correspond to SMC stars. Example evolutionary tracks computed with
MESA for LMC composition (see Appendix A) are shown by black lines, with the
corresponding evolution of the acoustic cutoff frequency shown in the bottom
panel. Different line styles correspond to different initial stellar masses as
indicated by the legend. The combined predicted excited frequency ranges for a
20 and 25 M⊙ star from Fig. 5 of Saio et al. (2013) at solar metallicity are
shown as a function of $\log T_{\rm eff}$ for pre-RSG (hatched grey) and post-
RSG (light grey) evolution, respectively.

Motivated by these prospects, Dorn-Wallenstein et al. (2022, hereafter DW22)
set out to identify additional FYPS stars in the large and small Magellanic
Clouds (LMC and SMC). The positions of their 17 candidate FYPS stars in the HR
diagram are shown in the top panel of Fig. 1 and compared to non-rotating
stellar evolution tracks of 15-35 M⊙ stars of LMC composition. The highest-
amplitude signals are shown as a function of effective temperature in the
bottom panel of Fig. 1, and they generally have higher frequencies than the
acoustic cutoff frequencies of the models shown by the black curves. Above
this cutoff, pressure modes are no longer reflected and trapped inside the
stellar interior, but become travelling waves and dissipate. Details of these
calculations are provided in Appendix A. For comparison, we also show the
combined predicted frequency ranges of excited modes of a 20 and 25 M⊙ star
derived by Saio et al. (2013) before (hatched grey) and after (light grey) the
red supergiant (RSG) evolutionary stage assuming solar metallicity, which the
highest-amplitude FYPS frequencies also exceed.

The work by DW22 included a renewed appreciation for possible source confusion
due to blending of multiple sources in the 21″ pix-1 TESS images. Comparing
their detected frequencies to signals detected in OGLE light curves (Udalski
et al., 2015) of nearby stars, they reject that several individual signals are
intrinsic to the YSGs. Two of the original five FYPS stars (HD 269110 and HD
269902) were found to be contaminated as a result, along with roughly half of
their initial sample of TESS variable light curves. Remaining signals that
cannot be attributed to other OGLE sources are interpreted as being intrinsic
to the YSGs and used to classify these objects as FYPS. The authors argue that
a statistically significant excess of variable light curves extracted for
stars with $\log{L/L_{\odot}}>5$ supports that FYPS are not purely the result
of contamination.

We demonstrate in this work that the TESS data themselves show additional
signals for the 17 FYPS stars identified by DW22 to originate from other
contaminating sources. We utilize the Python package TESS_localize (Higgins &
Bell, 2023) to fit the source locations for the strongest signals reported for
these objects. Most of these signals are too weak in individual TESS sectors
to be localized, but every signal that can be localized is shown to be
significantly offset from the YSGs (except for BZ Tuc, which is a long-period
Cepheid variable). This includes two more of the original five stars used to
define the FYPS class, HD 269953 and HD 268687. We argue that FYPS should not
be considered a unique region of the pulsational H-R diagram until pulsational
variability can be uniquely attributed to YSGs. This case study demonstrates
the importance of using the TESS pixel data to assess potential contamination
when interpreting any signals detected by TESS given its large plate scale.

##  2 The case of HD 269953 (TIC 404850274)

Expanding the sample to 17 FYPS, DW22 no longer provide the full prewhitening
solutions as were in their previous papers. Instead they indicate the
approximate frequency of the highest amplitude signal that they associate with
each YSG, which they call $f_{0}$. This is after they reject signals that they
are able to attribute to different OGLE sources. We detail our analysis of the
prototypical FYPS star HD 269953 (TIC 404850274) here to demonstrate how we
interpret their work.

HD 269953 was one of the first YSGs found to show pulsational FYPS
variability, with DW19 reporting 14 frequencies of variation. Four frequencies
are reported in DW20: 1.593, 1.174, 1.335, and 2.671 d-1, in order of
decreasing amplitude. Changes in the prewhitening procedure and how the
additional stochastic low-frequency variability is handled is likely the
reason for the change in extracted frequencies. The last two reported
frequencies are a harmonic pair that are likely associated with the same
physical process. Table B1 of DW22 reports that HD 269953 has six signals,
with the 2.671 d-1 peak having the highest amplitude ($f_{0}$). The
periodogram shows additional significant peaks that do not appear to have been
considered by these works, some of which are of higher signal-to-noise (S/N)
ratio than the extracted frequencies. Here we investigate the four signals
from DW20, which includes $f_{0}$ and its subharmonic. Figure B1 in DW22111The
arXiv version 2206.11917v3 shows the frequencies associated with nearby
contaminants as red, vertical, dashed lines for HD 269953 in their Fig. B1.
implies that they find that the previously-dominant 1.593 and 1.174 d-1
signals can be ascribed to other OGLE sources.

Higgins & Bell (2023) developed a method that utilizes the high frequency
resolution of TESS to mitigate source confusion challenges caused by its low
spatial resolution. They demonstrate that the amplitudes of observed
variations (modeled as sinusoids) measured by each individual pixel is
proportional to the flux from the variable source recorded by that pixel. The
distribution of best-fit amplitudes can be fit with the TESS pixel response
function (PRF) model (Bryson et al., 2010) to constrain the position of the
variable star on the sky.

The localization method is implemented in an open-source Python package,
TESS_localize,222https://github.com/Higgins00/TESS-Localize that we use to
analyze the signals observed in the light curve of HD 269953. The code takes a
TESS Target Pixel File and observed frequencies of variability as inputs, and
returns a best-fit source location. For best results, TESS_localize users are
encouraged to validate the quality of the output; we reject all results with
fitted PRF amplitudes less than five times their reported uncertainties
(insignificant detections) or a reduced $\chi^{2}>20$ for the fit (poor fit
agreement; see discussion in Higgins & Bell 2023). If the localization with
the aperture used by the TESS Science Processing Operations Center (SPOC)
pipeline does not return a satisfactory result, we try again with the
“autoaperture” convenience function, which can produce better results if most
of the signal is located outside the pipeline aperture. We let TESS_localize
attempt to automatically determine an appropriate number of principal
components to use to detrend the light curves.

Besides the pair of harmonic signals, there is no reason to assume that all
detected signals originate from a single source in the blended TESS
photometry. We run the pair of harmonics through TESS_localize together and
the two other signal frequencies individually. We attempt to localize these
signals in each of the 23 TESS sectors of two-minute-cadence data available
between Sectors 1 and 39. Considering the fits that pass our quality criteria
(the majority for each signal), each frequency of variation gets localized to
a consistent but different location on the sky. All are well separated from
the YSG by more than a pixel, with a fit precision of $\approx 0.1$ pix.

Figure 2: Median TPF flux of TESS sector 34 for the YSG star HD 269953 (TIC
404850274, red star) and positions of three nearby contaminating stars shown
in grey, pink, and blue. These points mark the average locations obtained for
each signal across 23 sectors, with error bars representing 3 $\sigma_{\rm
std}$. Bottom panels provide the first half of each extracted light curve
(left; corresponding to one spacecraft orbit) and associated periodograms
(right) for the five different pixel masks indicated in the top panel. The
frequency values of the three independent signals identified by DW20 based on
the SPOC PDCSAP light curves (yellow) are shown by vertical dashed lines in
the periodograms. See text for further details.

Figure 2 displays all the reliable source locations obtained by TESS_localize
plotted over the TESS Sector 34 Target Pixel File (TPF) in the top panel. The
position of HD 269953 on the TPF is indicated by the red star, while the
aperture mask used to extract the 2-min cadence light curve by the SPOC
pipeline is shown by the hatched yellow region. Average fit locations
corresponding to each of the three independent frequencies are presented with
white circles with three different fill colors, including their 3 $\sigma_{\rm
std}$ as error bars. The average (RA, Dec) fit coordinate for the 1.593 d-1
signal shown in grey is (85.0370, -69.6726) in decimal degrees (23.7″ from the
YSG). The 1.174 d-1 signal (pink) is centered on (85.0160, -69.6693), and the
1.335 d-1 and its harmonic $f_{0}$ (blue) are localized to (85.0197, -69.6638)
degrees (43.2″ and 41.5″ from the YSG, respectively). Figure 2 also shows the
locations of known Gaia sources down to a $G$-magnitude of 17.

The bottom panels of Figure 2 display the light curves and their periodograms
extracted with different apertures, color-coded to match the outlined
apertures in the example image. Details on how the light curves were extracted
and normalized are given in Appendix B. The first row shows the Pre-search
Data Conditioning Simple Aperture Photometry (PDCSAP) light curve and
periodogram from the TESS SPOC pipeline aperture; the three main signals are
marked in the periodogram with dashed vertical lines. Restricting the aperture
to the two pixels containing most of the light from the target HD 269953, the
next row shows the same signals to be absent. Extracting light curves from the
individual pixels containing the average TESS_localize fit locations for the
three independent signals for the next three panels confirms where these
signals are observed to be strongest. Different signals varying in amplitude
differently across pixels is a telltale sign of blended variable light curves
(Colman et al., 2017).

Figure 3: Light curves from the left-hand panels of Fig. 2 phase folded by one
half of the three independent frequencies 1.174 d-1 (left), 1.335 d-1
(center), and 1.593 d-1(right) identified by DW20 for HD 269953, and
corresponding to the three vertical dashed lines in the right hand panels of
Fig. 2. The black dotted curves show the average flux calculated in 0.05 phase
bins. We note again that DW22 had already found 1.174 d-1 and 1.593 d-1 to
originate from nearby contaminants.

Figure 3 shows the light curves from the left hand panels of Fig. 2 phase
folded by the half value of the three independent frequencies 1.174 d-1
(left), 1.335 d-1 (center), and 1.593 d-1 (right). As previously mentioned,
the 1.174 d-1 and 1.593 d-1 signals were already associated by DW22 to nearby
OGLE sources known to be eclipsing binaries (OGLE LMC-ECL-21974 and OGLE LMC-
ECL-22011 with $V=15.859\,$mag and $V=15.1\,$mag, respectively), and both
correspond to the second harmonic of their orbital frequencies (Pawlak et al.,
2016). The eclipses can clearly be seen in the light curves centered on the
two OGLE sources (pink and grey) when they are folded on their corresponding
orbital frequencies, and are also visible (but weaker) in the light curves
extracted from the SPOC pipeline aperture. This is also represented in the
differences between the amplitudes of the signals shown in the periodograms in
Fig. 2. In comparison, the signal does not show up in the red phase-folded
light curves that contains a higher fraction of light from the YSG target.

The source location of the 1.335 d-1 signal coincides with the O-type star BI
265 ($V=12.375\,$mag). Phase folding the light curve by $\frac{1}{2}\times
1.335$ d-1 reveals two clear eclipses that are not obvious in the light curve
of the YSG ($V=9.95\,$mag). While BI 265 has not previously been identified as
a binary star, this result is not surprising given the expected high binary
fraction for O-type stars (Sana et al., 2013; Kobulnicky et al., 2014). We
note that while all three identified sources are significantly fainter than
the YSG target ($2.4-5.9$ mag in the V-band), their high-amplitude variability
signals are still able to contaminate the light curve of the YSG.

It is clear that none of the signals reported for HD 269953 from DW20
originate from the YSG target.

##  3 Localizing the FYPS signals

As demonstrated in detail for the FYPS prototype HD 269953 above, we can use
TESS_localize to fit the sky positions of signals reported to belong to FYPS
pulsators. Most of the FYPS signals are only detectable with multiple sectors
of data; since TESS_localize can only fit a source location in a single sector
at a time, it cannot reliably localize such weak signals. For signals that are
strong enough to be detected in individual sectors, multiple sectors of data
enable multiple independent localizations of the same signals. Finding
consistent source locations across multiple sectors verifies the reliability
of the results, especially since images from different sectors are oriented
differently on the sky. The $f_{0}$ value provided in Tables B1 and B2 of DW22
is the frequency of the highest-amplitude peak that they associate with each
star in their sample. We attempt to recover these $f_{0}$ signals to full
precision following a similar prewhitening methodology.

For each YSG star, we downloaded the 2-min cadence SPOC light curves from the
Mikulski Archive for Space Telescopes (MAST) for all available sectors using
the lightkurve Python package. The specific observations analyzed can be
accessed via the following DOI:https://doi.org/10.17909/tckv-fb67 (catalog
10.17909/tckv-fb67). Following DW22, we used the PDCSAP flux light curves,
which have had corrections applied to mitigate systematic trends, and we
divided the flux in each sector by its corresponding median before combining
data from all available sectors. These light curves should be identical to the
ones used by DW22. Subsequently, we changed the flux units to parts-per-
thousand (ppt), centered the light curves around zero, and carried out an
iterative prewhitening following a similar procedure adopted by Pedersen et
al. (2021), where the highest S/N signals are removed first using publicly
available time series analysis Python packages from the IvS
repository.333https://github.com/IvS-KULeuven/IvSPythonRepository Except for
HV 829, we limited the prewhitening to frequencies below 10 d-1 and stopped
once $S/N<4$, calculated within a 1 d-1 window of the extracted frequency.
This is a lower S/N threshold than is advised for general signal detection in
such extensive light curves (Baran & Koen, 2021), but it is useful here where
we are aiming to recover signals at specific frequencies. The resulting
extracted frequency lists were filtered for close frequencies using the Loumos
& Deeming (1978) resolution criterion of $2.5/T$, where $T$ is the length of
the light curve. We crossmatched this final list of frequencies with the
tabulated $f_{0}$ values from Table B1 and B2 of DW22, in order to recover the
reported $f_{0}$ values to a higher precision.

=0.5in

Table 1: List of frequencies used to carry out the source identification with
TESS_localize for the 17 FYPS stars.

TIC ID | Common name | $N_{f}^{\text{DW}}$ | $f_{0}^{\text{DW}}$ | $N_{f}$ | freq. | Combination
---|---|---|---|---|---|---
|  |  | (d-1) |  | (d-1) |
29984014 | HD 268687 | 6 | 2.765 | 13 | $f_{0}=2.76526$ |
31106686 | HD 33579 | 13 | 0.177 | 1 | $f_{0}=0.17713$ |
31109182 | HD 268946 | 8 | 0.168 | 6 | $f_{0}=0.16846$ |
179304909 | SK -69 99 | 2 | 0.292 | 5 | $f_{0}=0.29210$ |
276863889 | HD 269787 | 2 | 0.909 | 9 | $f_{0}=0.90868$ |
276864037 | HD 269781 | 13 | 0.072 | 3 | … |
276869010 | HD 269762 | 4 | 0.176 | 7 | $f_{0}=0.17614$ |
277108449 | HD 269840 | 3 | 0.717 | 13 | $f_{0}=0.71703$ |
279956577 | HD 269604 | 1 | 0.105 | 10 | $f_{0}=0.10522$ |
|  |  |  |  | $f_{1}=0.09012$ |
|  |  |  |  | $f_{2}=0.19419$ | $f_{0}+f_{1}$
279957325 | CD-69 310 | 13 | 0.101 | 10 | $f_{0}=0.10070$ |
391813303 | HD 269651 | 2 | 0.098 | 4 | $f_{0}=0.09828$ |
391815407 | HD 269661 | 21 | 4.784 | 15 | … |
404850274 | HD 269953 | 6 | 2.671 | 21 | $f_{0}=2.67059$ |
425083216 | HD 269723 | 2 | 2.374 | 6 | $f_{0}=2.37353$ |
181043309 | HV 829 | 30 | 29.893 | 5 | … |
181446366 | [VA82] II-2 | 1 | 0.899 | 6 | $f_{0}=0.90173$ |
|  |  |  |  | $f_{1}=1.80015$ | $2\,f_{0}$
267547804 | BZ Tuc | 4 | 0.183 | 1 | $f_{0}=0.18212$ |

Note. — The TIC IDs of the stars are listed, followed by their common name.
The first 14 stars are LMC targets, while the last three are from the SMC. The
number of prewhitened frequencies identified by DW22 is denoted as $N_{f}^{\rm
DW}$, while $f_{0}^{\rm DW}$ is the corresponding highest amplitude frequency
that they recover and do not attribute to a contaminating star. $N_{f}$ is our
number of prewhitened frequencies. The sixth column lists the closest
frequency from our list of extracted frequencies that match with the
corresponding $f_{0}^{\rm DW}$ within the Rayleigh limit, as well as related
frequencies used in our TESS_localize analysis. Empty entries means that no
frequencies matched with $f_{0}^{\rm DW}$ within the Rayleigh limit. For the
stars with multiple frequencies listed, the last column denotes how they are
related.

In 3 out of 17 cases, we were unable to identify a significant periodogram
peak within the Rayleigh limit ($\sigma_{R}=1/T$) of the tabulated $f_{0}$
values. We attribute this to be due to differences in our adopted prewhitening
and frequency filtering procedures. For HD 269781, the $f_{0}$ signal was
excluded from our initial extracted frequency list when filtering for close
frequencies due to a higher amplitude signal being present at 0.0648 d-1. By
lowering our S/N stopping criterion, the $f_{0}$ signal for HD 269661 could be
extracted (4.78414 d-1, $S/N=2.963$), while a signal at 29.85982 d-1
($S/N=2.40$) within $1.65\,\sigma_{R}$ of $f_{0}$ could be found for HV 829.

We identify signals that are arithmetically related to $f_{0}$ (e.g., integer
multiples, sums or differences) as either belonging to the same harmonic
sequence or a set of combination frequencies. These signals are likely to be
physically associated with the same source, as it is unlikely for unrelated
signals to fall within frequency bins that are related in these ways by chance
given the high frequency resolution of TESS (finer than 0.003 d-1 for stars in
the TESS continuous viewing zones). The crossmatched $f_{0}$ values and
associated combination frequencies used for TESS_localize are listed in Table
1.

Of the fourteen stars for which we can confirm a significant peak at $f_{0}$,
we obtain at least one fit meeting our quality criteria for six. Four of these
have consistent source locations returned for multiple sectors, though the
signal reported for BZ Tuc appears not to be astrophysical upon further
scrutiny. We summarize the results for each of the six stars below.

###  3.1 HD 269953

HD 269953 was analyzed in detail in Section 2. The $f_{0}$ signal and its
subharmonic are offset from the YSG target by 41.5″ and coincide with the
O-type star BI 265. Localization of these signals met our reliability criteria
in 22 out of 23 available sectors of TESS data.

###  3.2 HD 268687

HD 268687 ($V=10.73$ mag) returned good fits for 20 out of 25 sectors, all
consistent with an average location of (72.7433, -69.4356) degrees, which is
20.5″ from the target, see Fig. 4. This position is most consistent with a
known eclipsing binary, OGLE LMC-ECL-1544 ($V=16.043$ mag), with an orbital
period of 2.169763 days (Graczyk et al., 2011), of which $f_{0}$ is the 6th
harmonic. The second column of panels in Fig. 4 shows the three extracted
light curves from SPOC, the target, and the identified source of the $f_{0}$
signal, phase folded by $\frac{1}{6}f_{0}$. The binned averages shown in black
reveal the eclipses of the OGLE LMC-ECL-1544 binary, which are otherwise
difficult to see due to the noisy TESS data. For comparison, we show in Fig. 5
the phase folded TESS light curve (top panel) and the corresponding phase-
folded OGLE $V$ and $I$-band light curves (two bottom panels) of the eclipsing
binary, where the eclipses show up much more clearly in the OGLE data. As TESS
is designed for observing bright targets, this difference is not unexpected
given the faintness of the binary. Nevertheless, we note in spite of the
contaminating star being more than five magnitudes fainter than the target
YSG, the eclipsing binary variability is still influencing the SPOC light
curve.

Figure 4: Median TPF flux of TESS sector 28 for the YSG star HD 268687 (TIC
29984014, red star) and position of a nearby contaminating star indicated by
the white cross. Bottom panels show the extracted light curve (left), the
phase folded light curves using $\frac{1}{6}f_{0}=0.460877$ d-1 (center), and
the periodograms (right) for the three different pixel masks indicated in the
top panel. The $f_{0}$ value of the the highest amplitude independent signal
identified by DW22 based on the SPOC aperture (yellow) is shown by vertical
dashed line in the periodograms. Figure 5: Phase binned light curves of OGLE
LMC-ECL-1544 using the 2-min cadence TESS data (top panel; Same as bottom
center panel of Fig. 4), and the OGLE V (middle) and I (bottom) band
photometry (Udalski et al., 1997; Szymanski, 2005). The light curves were
phases folded assuming $f_{\rm orb}=\frac{1}{6}f_{0}=0.460877$ d-1. The black
curves show the average flux in 0.01 (top), 0.02 (middle), and 0.01 (bottom)
phase bins.

###  3.3 HD 33579

HD 33579 has 12 sectors of TESS data available and TESS_localize reported a
marginally significant result for only Sector 29. The data from that sector
shows considerable systematic noise, which can confuse localizations,
especially for such low-frequency signals that only complete a few cycles per
sector. Combined with a lack of corroboration from other sectors, we interpret
this single “good” fit as spurious.

###  3.4 HD 268946

HD 268946 returns three localizations that pass our initial quality criteria
out of twelve; however, we reject them as spurious detections since they are
found at inconsistent sky locations. Inspecting the light curves suggests that
the fits are coupling to TESS systematics with similar timescales as the
alleged signal.

###  3.5 HD 269787

HD 269787 ($V=10.73$ mag) data yield six good localizations out of ten
available sectors of data, all at consistent sky locations. The source of the
$f_{0}$ signal is centered on (83.6215,-66.9711) degrees on average, which is
31.5″ from the position of the YSG target as shown in Fig. 6. The reported
signal can be uniquely ascribed to the object AL 327 (TIC 276863886, $V=14.80$
mag), an emission-line star (Andrews & Lindsay, 1964; Howarth, 2013) not
previously studied as a photometric variable. We note that the contaminating
star is three magnitudes fainter than the YSG.

Figure 6: Median TPF flux of TESS sector 28 for the YSG star HD 269787 (TIC
276863889, red star) and position of a nearby contaminating star indicated by
the white cross. Bottom panels show the extracted light curve (left), the
phase folded light curves using $f_{0}=0.90868$ d-1 (center), and the
periodograms (right) for the three different pixel masks indicated in the top
panel. The $f_{0}$ value of the the highest amplitude independent signal
identified by DW22 based on the SPOC light curves (yellow) is shown by the
vertical dashed line in the periodograms.

###  3.6 BZ Tuc

BZ Tuc has two sectors of data available, and TESS_localize localized the main
reported signal to the target in both, as shown in Fig. 7. This is a fairly
well studied Cepheid variable with one of the longest known periods of 127
days (as HV 821, e.g., Gascoigne & Kron, 1965; Eggen, 1977). In general, it is
difficult to reliably measure intrinsic periods of variation close to or
exceeding the TESS orbital period of 13.7 days, as this is a typical timescale
of TESS systematics, and TESS light curves show significant systematic
differences in flux zero points between sectors. This limitation of the TESS
data has been borne out in efforts to measure stellar rotation periods (Canto
Martins et al., 2020; Avallone et al., 2022; Holcomb et al., 2022).

Figure 7:  TESS localization result for BZ Tuc (TIC 267547804), showing that
the $f_{0}$ signal identified by DW22 coincides with the position of the YSG
on the TPF. Positions of nearby Gaia sources brighter than 17 mag are also
shown.

Figure 8 shows both types of light curves produced for BZ Tuc by the TESS SPOC
pipeline for sector 27 (left) and 28 (right): the simple aperture photometry
(SAP) light curves that are directly extracted from the target aperture (top),
and the PDCSAP light curves that have been further processed in an attempt to
mitigate observational systematics (middle). These light curves were
normalized separately for each sector by dividing by the median flux in the
sector, centering around zero, and then changing to units of ppt. The long-
timescale Cepheid variability is visible in the SAP light curves, but
conspicuously absent in the PDCSAP light curves, which are instead dominated
by systematic errors. The additional light curve detrending of the PDC
algorithm in the SPOC pipeline fits and removes combinations of cotrending
basis vectors (CBVs) from the SAP light curves. CBVs represent systematic
trends that principal component analysis reveals to be most common among TESS
light curves (Kinemuchi et al., 2012). The PDCSAP light curves are what
DW19–DW22 worked with, and what we also analysed to reproduce their work.
Observational systematics characterized by the CBVs often vary on similar
timescales as the observing run duration or spacecraft orbit that can mimic
long-timescale astrophysical signals. Fitting CBVs to such targets tends to
over-fit the data, removing the astrophysical signals of interest while
introducing or amplifying other systematics from the residuals of the CBV
fitting. For these reasons, using the CBV-corrected light curves for long-
period variables like BZ Tuc is not advised (Kinemuchi et al., 2012). For the
BZ Tuc light curves, the PDC pipeline opted to use the Multi-Scale correction
method (Stumpe et al., 2014), even though the Single-Scale option (Smith et
al., 2012) tends to better preserve long-timescale signals.

The bottom panels of Figure 8 show the periodograms of the two PDCSAP (black)
and SAP (grey) light curves separately for each sector, with the reported
$f_{0}$ signal indicated (red dashed line). The $f_{0}$ only appears as a
compelling peak in the PDCSAP light curves, which have been overcorrected by
the TESS pipeline. But TESS_localize extracts the light curves from each
pixel, and it still localized this signal to BZ Tuc. As an optional step,
TESS_localize does consider applying its own PCA corrections to the extracted
light curves, and in this case it recognized that the CBVs it computed contain
significant power at the frequency of interest so it opted not to risk
applying these corrections. Still, the long-timescale variations observed in
these pixels does include some power from the Cepheid pulsations (and
potentially also systematics) at the spurious $f_{0}$ frequency—the gray
periodograms of the SAP light curves show slightly elevated amplitudes at this
frequency compared to the average noise level observed at higher frequencies.
This power excess at $f_{0}$ from the longer-timescale Cepheid variability
caused the signal to be localized to BZ Tuc despite it not being an unique
independent pulsation signal of this star. This highlights one of the failure
modes of TESS_localize, due to the violation of a base assumption: that the
input frequencies represent significant and unique signals from one source in
the field.

Figure 8: SAP (top panels, grey) and PDCSAP (middle panels, black) light
curves of BZ Tuc for the two available 2-min cadence sectors. The bottom
panels show the periodogram of PDCSAP and SAP light curves with the $f_{0}$
signal indicated by the dashed red line. Due to the different amplitude scales
of the PDCSAP and SAP periodograms, the SAP amplitudes are shown in grey on
the right-hand sides of both bottom subplots in units of ppt.

##  4 Conclusions

Of the first five YSGs that DW20 used to argue the existence of a new FYPS
class of pulsating variable star, DW22 attribute the variability of HD 269110
and HD 269902 to contaminants based on OGLE data (TESS_localize confirms). We
have shown that the main signals from HD 269953 and HD 268687 also originate
from other sources. DW22 found the 1.135 day-1 signal that DW20 identified as
the strongest for the remaining candidate, HD 269840, to be caused by
contamination, which we confirm with TESS_localize. The remaining variations
in the light curve that DW22 associate with HD 269840 are too weak for
TESS_localize to locate, but there is no reason to assume that they belong to
the YSG in such a crowded part of the sky.

Of the 14 YSG stars with a confirmed significant peak at the $f_{0}$ signals
reported by DW22, we find consistent source locations for four of them,
including the previously mentioned HD 269953 and HD 268687 stars. For three of
these, the $f_{0}$ signals are associated with nearby contaminating star,
while the signal for known Cepheid variable BZ Tuc is localized to the target.
In the latter case, we find that the $f_{0}$ signal is likely a spurious
signal introduced by the PDC algorithm of the SPOC pipeline to the PDCSAP
light curve when removing the long-period Cepheid variability from the SAP
light curve. Finally, while DW22 make a statistical argument that all claimed
FYPS are unlikely to be caused by contamination, we argue that FYPS should not
be considered a class of pulsating star until rapid pulsational variability
can be uniquely associated with a YSG.

This work demonstrates how much of a challenge source confusion can be for
analyses of TESS data. Even if contamination of the aperture is predicted to
be low (estimated by the CROWDSAP header value), significant signals can still
be caused by source blending (Higgins & Bell, 2023). As seen in this work,
signals of nearby variable stars can contaminate light curves even when they
are more than five magnitudes fainter than the target stars. Interrogating
TESS data at the pixel level for contamination issues is essential if
misattribution of signals is to be avoided; the lightkurve Python package can
help to make the pixel data more accessible (Lightkurve Collaboration et al.,
2018). Statistical arguments for the likelihood of contamination of TESS light
curves may not be reliable. For localizing (multi-)periodic sinusoidal
variability to sub-pixel precision, the Python tool TESS_localize can help in
many cases (for guidance, see Higgins & Bell, 2023).

The authors are grateful to Jim Fuller, Lars Bildsten, Tim Bedding, Conny
Aerts, and Trevor Dorn-Wallenstein for their valuable discussions and comments
at different stages of the manuscript. We thank the referee for their comments
which improved the manuscript. This research was supported in part by the
National Science Foundation under Grant No. NSF PHY-1748958 as well as through
the TESS Guest Investigator program Cycle 4 under Grant No. 80NSSC22K0743 from
NASA and by the Professor Harry Messel Research Fellowship in Physics
Endowment, at the University of Sydney. This research benefited from
interactions with Lars Bildsten and Jim Fuller that were funded by the Gordon
and Betty Moore Foundation through Grant GBMF5076. This research made use of
Lightkurve, a Python package for Kepler and TESS data analysis (Lightkurve
Collaboration et al., 2018). This paper includes data collected with the TESS
mission, obtained from the MAST data archive at the Space Telescope Science
Institute (STScI). Funding for the TESS mission is provided by the NASA
Explorer Program. STScI is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS 5–26555. This research
has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.
This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

##  Appendix A MESA setup

For the construction of Fig. 1 we computed non-rotating stellar evolution
tracks for five different initial stellar masses (15 M⊙, 20 M⊙, 25 M⊙, 30 M⊙,
35 M⊙) using the stellar structure and evolution code MESA version 22.11.1
(Paxton et al., 2011, 2013, 2015, 2018, 2019; Jermyn et al., 2022). The models
were evolved from the Hayashi track to the end of core He burning, assuming an
initial stellar mass fraction for hydrogen, helium, and metals of $X=0.7391$,
$Y=0.2562$, and $Z=0.0047$ for the LMC following Köhler et al. (2015), who
based these values on the observed abundances of young massive stars in the
LMC (Brott et al., 2011). The Asplund et al. (2009) metal mixture and
corresponding OP opacity tables were adopted. We used the Ledoux criterion
with time-dependent convection, and adopted a small amount of convective
boundary mixing following the exponential diffusive overshoot formalism
(Freytag et al., 1996; Herwig, 2000). Finally, we included mass loss from the
Vink et al. (2001) hot wind scheme assuming a scaling factor of 0.3 (Björklund
et al., 2021). The full MESA inlist is available at
DOI:https://doi.org/10.5281/zenodo.7773563 (catalog 10.5281/zenodo.7773563).

##  Appendix B Light curve extraction and correction for the HD 269953 example

The light curves and associated periodograms shown in Fig. 2 were obtained in
two different ways. For the SPOC target pixel mask indicated by the hatched
yellow region in the top panel of the figure, we downloaded the SPOC 2-min
cadence PDCSAP flux light curve from MAST using the lightkurve Python package.
The downloaded light curve was subsequenctly normalized by dividing by the
median flux of the sector, and the flux units changed to parts-per-thousand
(ppt). Finally, the light curve is centered around zero and the Lomb-Scargle
periodogram calculated. These median normalized SPOC PDCSAP flux light curves
correspond to the ones analyzed by Dorn-Wallenstein et al. (2019, 2020, 2022).

For the remaining four pixel masks, the light curves were extracted and
corrected manually once again relying on lightkurve and its
RegressionCorrector class. The four light curves were extracted using simple
aperture photometry for the selected target pixel mask of HD 269953 (red) and
three pixel masks for the three contaminating stars shown in grey, pink, and
blue in Fig. 2. The background flux was extracted by creating a background
pixel mask, where all pixels fainter than 0.001 times the standard deviation
above the overall median flux in the TPF were included. To subsequently reduce
the dimensionality of the design matrix of the background flux used for the
linear regression, a principal component analysis was performed where the
dominant flux variability of the background pixels were captured using up to
five principal components.

Using the constructed design matrix, the extracted target and contaminator
light curves are corrected by creating a model of the background flux using
linear regression and subtracting the model from the uncorrected light curves.
Finally, the corrected light curves are normalized using a low order
polynomial (typically 1st order but up to 3rd depending on the sector) and
centered around zero after changing the flux units to ppt. The final light
curves and associated periodograms for Sector 34 are shown in the six bottom
panels of Fig. 2. The same methodology was adopted to extract and correct the
light curves shown in Figs. 4 and 6.

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