(Sato et al., 2005). Two stars showed typical errors of $3-7\ \rm{m\>s^{-1}}$
and negligible RV difference pre- and post-earthquake for stars that emerged
in OPSP.

To search for instrumental variations, we calculated GLS periodogram of the
full RVs of the three RV standard stars. As shown in Figure 43, we could
discover a significant variation of approximately two months from RVs of both
$\tau$ Cet and $\iota$ Per with estimated amplitudes of $\lesssim 3\rm{m\
s^{-1}}$. However, such a variation could not be derived from $\epsilon$ Vir
RVs and some previous studies on $\tau$ Cet, e.g., the planet discovery of
$\tau$ Cet with HARPS and Keck (Feng et al., 2017). Therefore, we infer that
the two-month variation with low amplitude might be introduced from the
instrument itself.

As for the stability of HIDES over 20 years, it was diagnosed by RVs of $\tau$
Cet for its mild RV variation and long-term stability. We re-extracted the RVs
obtained by HIDES-S, -F1, and -F2 with the same reference spectrum, and we
empirically eliminated the RVs with observational errors over $6\ \rm{m\
s^{-1}}$. As shown in Figure 44, we could apparently observe an offset between
HIDES-S and (-F1 and -F2) at a maximum of $\sim 5\ \rm{m\ s^{-1}}$, and an
offset between HIDES-F1 and -F2 of $\sim 2.5\ \rm{m\ s^{-1}}$. In most cases,
we could ignore the instrumental RV offsets by setting them as free parameters
in the Keplerian orbital fit. In this study, it was not suggested to simply
ignore the RV offsets for stars showing astrometric accelerations, because we
could trace astrometric accelerations with long-term consecutive RV monitoring
based on a unified zero-point.

In the case of HIDES, however, the RV standard stars were sparsely observed by
HIDES-S and -F1. It was thus never a good strategy to fit and remove the
trends with lines or curvatures because of the overcorrection to the zero-
point. Instead, we could adopt a more moderate correction by ignoring the
slight instrumental RV variations inside individual observation modes but
shifting the RV offsets between individual modes based on the mean level. It
had two primary benefits in this study:

  * •

It did not influence the RV orbit fitting in Section 3.4 since, as mentioned
before, the RV offsets to an arbitrary zero-point in the Keplerian model were
set to be free parameters.

  * •

It moderately flattened the RV offsets between different observation modes so
that the RV variations of the revisited stars can be well described in the
longest time scale of 20 years.

This moderate correction was applied to four systems (HD 5608, HD 14067, HD
120084, and HD 175679; see Section 6) when we performed the joint constraint
with RV and astrometry.

Figure 42:  The RVs of $\tau$ Cet, $\iota$ Per, and $\epsilon$ Vir obtained by
HIDES-F2. Single measurements are marked by non-colored markers, and binned
measurements are marked by colored markers connected by dashed lines for
indication of trends. We use 20191201 to indicate the earthquake, and HIDES
was not scheduled between 2019 November 25th and 2019 December 6th.  Figure
43:  The GLS periodograms of RVs of $\tau$ Cet (left panel), $\iota$ Per (mid
panel), and $\epsilon$ Vir (right panel) obtained by HIDES-F2. In each panel,
we present the GLS periodograms of each star derived from different data sets
and the window function. In each subplot, we indicate FAP levels of 10%, 1%,
and 0.1% with the horizontal lines from bottom to top.  Figure 44:  The RVs of
$\tau$ Cet measured by a unified reference spectrum. Single measurements are
marked by non-colored markers, and binned measurements are marked by colored
markers.

##  Appendix B RV fitting results for normal stars

In this section, we present the Keplerian orbital solutions to the normal
stars, which are not concretely described in the main text (Section 4, 5 and
6). In Figure 45, 46, and 47, we present the orbits of single-planet systems,
including HD 2952, HD 4732, HD 16400, 6 Lyn, 4 Uma, o Uma, HD 104985, o CrB,
HD 145457, HD 173416, HD 180314, $\xi$ Aql, and HD 210702. In Figure 48, we
present the orbits of double-planet systems, including HD 4732, HD 47366,
$\gamma$ Lib, and $\nu$ Oph. Finally in Figure 49, we present the corner plots
of HD 5608, HD 14067, HD 120084, and HD 175679 from orvara orbit fitting.

Figure 45:  Keplerian orbital fit to HD 2952, HD 4732, HD 16400, 6 Lyn, and 4
Uma.

Figure 46:  Keplerian orbital fit to o Uma, HD 104985, o CrB, and HD 145457.

Figure 47:  Keplerian orbital fit to HD 173416, HD 180314, $\xi$ Aql, and HD
210702.

Figure 48:  Keplerian orbital fit to HD 4732, HD 47366, $\gamma$ Lib, and
$\nu$ Oph.

Figure 49:  orvara corner plot of HD 5608, HD 14067, HD 120084, and HD 175679.

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