Copyright for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).

Joint Proceedings of the ACM IUI 2021 Workshops, April 13–17, 2021, College
Station, USA

[orcid=0000-0003-1454-0641, ]

[orcid=0000-0002-8388-9137, ]

[orcid=0000-0001-9461-5804, ]

# Retrofitting Meetings for Psychological Safety

Marios Constantinides<EMAIL_ADDRESS>Sagar Joglekar
<EMAIL_ADDRESS>Daniele Quercia daniele.quercia@nokia-bell-
labs.com Nokia Bell Labs, Cambridge, UK  King’s College, London, UK

(2021)

###### Abstract

Meetings are the fuel of organizations’ productivity. At times, however, they
are perceived as wasteful vaccums that deplete employee morale and
productivity. Current meeting tools, to a great extent, have simplified and
augmented the ways meetings are conducted by enabling participants to “get
things done” and experience a comfortable physical environment. However, an
important yet less explored element of these tools’ design space is that of
psychological safety—the extent to which participants feel listened to, or
motivated to be part of a meeting. We argue that an interdisciplinary approach
would benefit the creation of new tools designed for retrofitting meetings for
psychological safety. This approach comes with not only research
opportunities—ranging from sensing to modeling to user interface design—but
also challenges—ranging from privacy to workplace surveillance.

###### keywords:

meetings execution physical comfort psychological safety

##  1 Introduction

Meetings are often considered as the fuel of an organization’s productivity.
Employees come together for a common purpose to discuss ideas, to make
collective decisions, and to ultimately reach their objectives. However, it is
no secret that meetings are often seen as wasteful vacuums, or as an enemy of
productivity. Although there are good meetings and bad meetings, their
collective negative impact on employee morale and productivity is significant
[1]. To moderate this, organizations devote notably large amounts of resources
to facilitate and support them. While meeting tools pledge to facilitate
better meetings—ones that are well-executed, and create a safe environment for
contribution—yet report after report estimate a growth of ineffective
meetings111https://www.forbes.com/sites/danielreed/2019/01/30/report-suggests-
that-23rds-of-the-100-billion-spent-annually-on-business-meetings-travel-is-
wasted; numbers though that are bound to change, if meeting tools were to
fully capture people’s meetings experience. Recently, in a large-scale
crowdsourcing study [2], researchers determined the main factors that impact
people’s meetings experience. They administered a 28-item questionnaire to 363
individuals whose answers were statistically analyzed through Principal
Component Analysis, and found that three factors sufficiently capture people’s
experience in meetings, namely, (a) execution, (b) physical comfort, and (c)
psychological safety. Put differently, these factors capture the extent to
which (a) people feel that a meeting was productive, (b) the meeting room was
pleasant, and (c) the setting was psychologically safe.

Current meeting tools, however, primarily focus on enabling participants to
“get things done” (i.e., _execution_), or on optimizing the environmental
conditions (i.e., _physical comfort_). Execution is about whether a meeting
had a clear structure, purpose, and resulted into a list of actionable items;
a large body of previous research focused on these aspects. Kim and Rudin [3]
developed a system that detects key decisions in dialogues, while McGregor and
Tang [4]’s system generates an ‘action items’ list from the spoken dialogue.
Using an agenda planning technique, Garcia et al. [5] allowed meetings
participants to vote for agendas to improve perceived meeting quality. Video
Threads [6] provides asynchronous video sharing, while Time Travel Proxy [7]
identifies the gist of what was missed to enable late participation
effectively. Physical comfort is about whether the meeting room was pleasant
(in regard to air quality and crowdedness). In Human-Building Interaction
literature [8], poor environmental conditions are known to impact employees’
cognitive functions, decision making, and performance. Therefore,
organizations have resorted to sensors through which the environmental
conditions could be sensed [2, 9], and even adapted accordingly [10] to meet
recommended standards, thus increasing their employees’ productivity and well-
being. To this end, meeting tools could account for physical comfort in their
design, potentially in a form of interventions (e.g., adjusting ventilation).
However, _the design space should not only facilitate execution and ensure
that desirable physical environmental conditions are met, but should also
cultivate a psychologically safe setting._

##  2 Capturing psychological safety

Psychological safety is about whether participants felt listened to, or
motivated to be part of a meeting. Edmondson described it “as the absence of
interpersonal fear that allows people to speak up with work-relevant content”
[11]. Previous research showed that inclusiveness and balance of
conversational turn-taking play an important role in group performance [12].
Tools have been developed to create awareness by highlighting salient moments
during conversations [13], to enhance group collaboration through persuasive
feedback [14], and to allow participants to reflect on their own and their
peers’ experiences [15]. Although such tools, to some extent, offer features
that facilitate execution and support physical comfort, they often fall short
in enabling psychological safety. We argue that a more interdisciplinary
approach would likely benefit the creation of new tools designed for
supporting psychological safety. To achieve that, we foresee a number of
challenges and opportunities, ranging from sensing to modeling to user
interface (UI) design.

Sensing. New emerging sensing devices such as earables [16] are now fully
equipped with IMU (inertial measurement unit) sensors, allowing on-body and
on-device sensing. This opens up a new avenue for meeting tools by allowing
participants to monitor signals that could otherwise go unnoticed; for
example, capturing body cues of (dis)agreement or (in)active participation
during a virtual conversation when the video stream is absent [17]. Similarly,
smartwatches are now fully equipped with heart rate sensors that provide a
window to people’s physiology, allowing one to track their own or their peers’
emotional states [18]; aspects that are closely linked to creating a safe
environment for contribution. Additionally, in the future, we foresee that
better precision devices would enable more nuanced non-verbal or verbal
communication patterns to be captured.

Modeling. New algorithms are also likely to provide a new understanding and
perspective that would help further theorize the concept of psychological
safety. New Natural Language Processing text-mining algorithms [19] are now
able to reveal certain language markers that might be deeply hidden in a
conversation, particularly in a remote setting. These algorithms can annotate
everyday language and capture important types of social interactions (e.g., a
heated discussion resulting in conflict resolution). NLP-based algorithms can
now analyze conversations and test whether these conversations accommodate
different points of view [20], or even reveal the presence (or absence) of
certain health-related markers (e.g., stress markers) [21]. Additionally, new
Natural Sound Processing algorithms [22] are now able to model verbal cues
(e.g., prosody) that would potentially enable richer and more focused
interactions. For example, prosodic features (e.g., pitch and energy) are
known to provide a reliable indication of the emotional status in a
conversational exchange.

UI design. Last but not least, new opportunities are likely to arise for the
UI design community. New visualizations are more likely to be (re)invented,
beyond dashboards and simple analytics [23]. Drawing from behavioral economics
research, we foresee that new forms of interventions would allow people to be
more empathetic, compassionate, and aware of each other’s emotional states,
views, and thoughts. Previous research in the area of organizational behavior
showed that affective sharing within groups conveys our internal experiences,
signals our emotional states and, potentially, makes us more aware and
empathic of each other [24]. Borrowing ideas from calm technology [25] and
biophilic design, meeting tools could embrace new types of cues only available
through technology [26]. For example, the use of different symbols, imagery,
and artificial artifacts (e.g., real-world objects [27], light [28], or
movement 222Blooming: http://www.thelisapark.com/blooming) could augment the
ways we interact and communicate with each other. These new visualizations
could bring teams together despite working apart, and remove any geographical
barriers due to physical distancing.

Workplace surveillance. While this interdisciplinary approach promises to
deliver experiences richer of psychological safety, it also raises questions
relating to workplace surveillance. It is often regarded that organizations
and surveillance go hand in hand [29]. On a very pragmatic level, there is a
handful of reasons as to why organizations opt in for employees’ surveillance
(e.g. maintaining productivity, monitoring resources used, protecting the
organization from legal liabilities). The critics, however, rightly argue that
there is a fine line between what organizations could be monitoring and what
they should be monitoring. If crossed, it will have consequences on employees,
affecting their well-being, work culture, and productivity. If future meetings
tools incorporate any kind of employees’ monitoring, they need to ensure that
is done in a way that preserves an individual’s rights, including that of
privacy.

The workplace is constantly changing and evolving. These changes are currently
accelerated by the COVID-19 pandemic, which might be leading to a dramatic
change in how we work: from the well-known eight-hour workday to the office
building to the salient boundaries between work and personal life. Meetings
are no exception to this sudden change. In a post-pandemic world, we envision
that new sensing devices would provide access to employees’ data that
otherwise might not be possible to collect (e.g., on-body sensing); that new
algorithms would ‘make sense’ of such data, and capture behavioral aspects
that are hard to quantify (e.g., (dis)agreement, empathy, or stress markers);
and that new user interfaces (e.g., inspired by biophilic design) would enable
meeting participants to stay connected despite any geographical or
technological barriers due to remote working.

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11institutetext: Max Planck Insititute for Radio Astronomy, Auf dem Hügel 69,
Bonn D-53121, Germany 11email<EMAIL_ADDRESS>22institutetext:
Department of Astrophysics, Institute for Mathematics, Astrophysics and
Particle Physics (IMAPP), Radboud University, PO Box 9010, 6500 GL Nijmegen,
the Netherlands 33institutetext: Department of Astronomy and Columbia
Astrophysics Laboratory, Columbia University, 550 W 120th Street, New York, NY
10027, USA 44institutetext: Center for Computational Astrophysics, Flatiron
Institute, 162 Fifth Avenue, New York, NY 10010, USA 55institutetext:
Department of Theoretical physics and Astrophysics, Faculty of Science,
Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

# Radio jet precession in M81*

S.D. von Fellenberg 11 M. Janssen 11 J. Davelaar 3344 M. Zajaček 55 S. Britzen
11 H. Falcke 22 E. Körding 22 E. Ros 11

(Received September 15, 1996; accepted March 16, 1997)

We report four novel position angle measurements of the core region of M81* at
5GHz and 8GHz, which confirm the presence of sinusoidal jet precession of the
M81 jet region as suggested by Martí-Vidal et al. (2011). The model makes
three testable predictions on the evolution of the jet precession, which we
test in our data with observations in 2017, 2018, and 2019. Our data confirms
a precession period of $\sim 7\leavevmode\nobreak\ \mathrm{yr}$ on top of a
small linear drift. We further show that two 8 GHz observation are consistent
with a precession period of $\sim 7\leavevmode\nobreak\ \mathrm{yr}$, but show
a different time-lag w.r.t. to the 5 GHz and 1.7 GHz observations. We do not
find a periodic modulation of the light curve with the jet precession, and
therefore rule out a Doppler nature of the historic 1998-2002 flare. Our
observations are consistent with either a binary black hole origin of the
precession or the Lense-Thirring effect.

###### Key Words.:

LLAGN – jet physics

##  1 Introduction

The galaxy M81 appears as a bright radio source and is located at a distance
of $3.36\pm 0.34\leavevmode\nobreak\ \mathrm{Mpc}$ (Freedman et al., 1994).
The black hole in the center of M81 belongs to the class of the low-luminosity
AGN (LLAGN) and exhibits relatively weak radio emission
($F_{\nu=4.8\mathrm{GHz}}\sim 150\leavevmode\nobreak\ \mathrm{mJy}$, e.g.:
Brunthaler et al. (2006)). It is the closest LLAGN to Earth. Due to its high
apparent luminosity, it serves as an optimal test-bed to characterize this
class of accreting black holes (Markoff et al., 2008). As such it may be the
best candidate to bridge the accretion processes of LLAGN and to that of Sgr
A* (GRAVITY Collaboration et al., 2020). M81 shows slow changes in radio flux
density on yearly time scales (e.g. Ho et al., 1999). Further, it shows fast
intra-day flare-like variability at mm-wavelengths (Sakamoto et al., 2001).
This radio and mm behavior is consistent with van der Laan expanding-blob-
scenario (van der Laan, 1966). Here, the mm-variability is created by blobs
that expand as they move along the jet, where they become observable in the
radio (Ho et al., 1999; Sakamoto et al., 2001). In the X-ray, M81 is detected
with luminosity of $\sim 10^{40}\leavevmode\nobreak\ \mathrm{erg/s}$, and flux
changes on the order of a few ten percent (Ishisaki et al., 1996). The overall
SED was modeled with a jet-dominated ADAF model by Markoff et al. (2008) using
a set of simultaneous multi-wavelength observations of M81 and shows
remarkable similarity to that of Sgr A* (e.g., von Fellenberg et al., 2018).

M81*, the core region of M81 is a regular target for global VLBI observations,
in particular since the explosion of the radio-luminous supernova SN 1993J
(Ripero et al., 1993; Weiler et al., 2007). This supernova was located at a
close angular separation to M81*, and was thus frequently used as a
calibration source. In VLBI observations, M81* is typically marginally
resolved and shows a jet in north-eastern direction. Bietenholz et al. (2000)
and Bietenholz et al. (2004) determined that M81 is at rest with respect to
SN1993J. Further, they found a frequency-dependent shift of peak-brightness of
M81*. This is consistent with the known core-shift-effect of many AGN jets
(Marcaide & Shapiro, 1984; Lobanov et al., 1998; Kovalev et al., 2008), which
is believed to be caused by synchrotron self-absorption of photons in the jet
plasma. In this picture, the apparent shift of the luminous component results
from the increasing opacity (and thus increasing luminosity) as function of
wavelength (Blandford & Königl, 1979; Konigl, 1981; Falcke & Biermann, 1995;
Marscher & Travis, 1996; Davelaar et al., 2018). M81* shows a decreasing core-
size ($\Theta$) as function of frequency, with an almost linear relationship:
$\Theta\propto\lambda^{\sim 0.9}$ (Bartel et al., 1982; Kellermann et al.,
1976; Bietenholz et al., 2000; Markoff et al., 2008). This relationship holds
down to mm-frequencies, with a confirmation at 43 GHz (Ros & Pérez-Torres,
2012), and one at 87 GHz (Jiang et al., 2018), which report a relation of
$\Theta\propto\lambda^{0.89\pm 0.03}$.

Martí-Vidal et al. (2011) confirmed the basic findings reported in earlier
works. They further showed that the M81* intensity peak is shifted as function
of frequency along the direction of the jet using VLBI measurements from 1993
to 2005. Its size increases with decreasing frequency. The authors determined
the location of the jet base to within $20\leavevmode\nobreak\ \mathrm{\mu
as}$ of the black hole, and constrained the black hole mass to $\sim 2\times
10^{7}\leavevmode\nobreak\ \mathrm{M_{\sun}}$ using the strongly-magnetized
accretion flow scenario (Kardashev, 1995). Alberdi et al. (2013) extend the
temporal baseline of observation to the year 2012 and confirmed the basic
findings reported in Martí-Vidal et al. (2011). By fitting elliptical Gaussian
models to the central source and, if detected, the jet component, they derived
a sinusoidal modulation of the jet position angle. They found a precession
period of $\sim 7\leavevmode\nobreak\ \mathrm{yr}$ on top of a linear increase
of the position angle by $\sim 0.5\mathrm{\degree/yr}$. They found this
precession to be present both in their 5 GHz observations, as well as in their
1.7 GHz observations. However, they found a lag of $1.9\pm 0.4$ years for the
precession between the frequency bands, which they interpreted as a core-shift
effect. In this picture, the jet shows a differential cork-screw-like
precession and different frequencies probe different regions along the jet.
Lastly, they connected the observed jet precession with a four year flare, and
argued that the increase in flux is caused by Doppler boosting of the jet
along the line of sight.

Their model therefore provides three testable hypotheses:

  1. 1.

A prediction of the position angle of the core component as function of time;

  2. 2.

A prediction of this modulation at different frequencies;

  3. 3.

A prediction of the expected flux level at a given time point.

In this letter, we investigate whether the three predictions hold against new
VLBI observations of M81* obtained in the years 2017, 2018, and 2019.

##  2 Observations and data reduction

In total we analyze four sets of observations of M81*. The first set, obtained
by the European VLBI Network (EVN) at 5 GHz in June 2017, was a dedicated
observation to measure the position angle of M81* (Prog. ID ED042, PI Jordy
Davelaar). The second set consists of an observation at 8 GHz obtained in June
2018 at the Very Long Baseline Array (VLBA) (Prog. ID BJ090, PI Wu Jiang),
with the intent to obtain phase-referenced observations of the core-shift
effect in M81*. Lastly, we used 5 GHz and 8 GHz VLBA observations obtained in
2019 dedicated to studying the jet-components in M81* (Prog. ID BJ099, PI Wu
Jiang). All data was reduced using the
rPicard111https://bitbucket.org/M_Janssen/picard. VLBI pipeline version v7.1.5
(Janssen et al., 2019), which makes use of CASA v6.5 (THE CASA TEAM et al.,
2022) and the latest VLBI features (van Bemmel et al., 2022)222For
reproducibility, the pipeline parameters are uploaded to
https://doi.org/10.5281/zenodo.7642852. To derive the position angle, we fit
all data with a single Gaussian model using Difmap (Shepherd, 1997). In all
cases, the source is marginally resolved; however, we opted for a simple
description by a singular Gaussian component to derive a robust measurement of
the position angle. Table 1 reports the dates, frequency bands, derived
values, and the respective imaging $\chi_{\rm{reduced}}^{2}$ values. The
corresponding maps and models are shown in Appendix D.

In order to obtain an as complete picture of M81* as possible, we have
searched the VLBA and EVN archives for available observations since 2012.
Several observations at higher frequencies exist, which we do not study in
this letter (e.g., BJ086, BB303). Three more observations in L, S, or X-band
exist: RP023A (EVN), RP023B (EVN), and BD185 (VLBA). Those, unfortunately, do
not allow a determination of the position angle as the data quality is not
sufficient. In RP023A, no long baseline stations participated in the
observations. In RP023B, several telescopes suffered from sensitivity losses
at the start of the scan, possibly due to being late on source. When the bad
measurements are flagged, the scan durations were no longer long enough to
obtain good fringe solutions. In BD185, we found large instrumental delay
corrections of $\sim$100 ns from the calibrator sources and only a few robust
fringe detections on M81 over the full Nyquist search window. These issues
possibly originate from an error in the clock search at the correlator.

We have further validated that we can reproduce the values published in
Alberdi et al. (2013) with one example (BB293 B), which gives consistent
results.

Date | Band | Position Angle $[\degree]$ | $\chi_{\rm{red}}^{2}$
---|---|---|---
2017-06-21 | C | 72.06 | 2.3
2018-06-10 | X | 81.06 | 1.9
2019-11-04 | C | 81.69 | 4.9
2019-11-04 | X | 73.00 | 3.8
Table 1: Date, observation band, derived position angle and reduced $\chi^{2}$
of the observation analysed in this study.

###  2.1 EVN Observation

We analyze a set of 5 GHz VLBI observations carried out by the EVN
observatory, which were obtained on the 21st of June, 2017 and which lasted
for about $12\leavevmode\nobreak\ \mathrm{h}$. The IR, YS, TR, SH, NT, MC, WB,
JB, and EF333Full name and location given in Table 5 stations participated in
the observations, and apart from a full loss of the RR polarization of the EF
station, no major technical difficulties occurred. The data were calibrated
using observations of J0958+6533.

###  2.2 VLBA BJ090 observation

We analyze the 8 GHz sub-set of the observations carried out in the VLBA BJ090
observation campaign from the 10th of June, 2018. The data included the BR,
FD, HN, KP, LA, MK, NL, OV, PT and SC stations and used OJ287, J0954+658 and
J1331+305 as calibration sources. No major technical difficulties occurred
during the observations, with overall good data quality. The data was reduced
in the same fashion as the EVN observations. Apart from 8 GHz observations
(X-band), the BJ090 observations included K-, Q-, and W-band observations
which we did not include in the analysis.

###  2.3 VLBA BJ099 observation

We analyze the 5 GHz and 8 GHz sub-sets of the observations carried out in the
VLBA BJ099 observation campaign, which was carried out on the 4th of November
in 2019. The data included the BR, FD, HN, KP, LA, MK, NL, OV, PT and SC
stations and used OJ287 and J0954+658 as calibration sources. While the 5 GHz
observations showed overall agreeable data quality, the 8 GHz data set
suffered from poor observations by the PT and SC stations. In order to derive
a position angle measurement in the 8GHz band, we excluded the baselines to
the PT and SC stations, the latter of which contributes the longest baselines.
For both observations, the fit is relatively poor, with reduced $\chi^{2}$
values between four and five. Apart from 5 GHz and 8 GHz observations (C-band
and X-band), the BJ099 observations included K-, Q-, and W-band observations
which we did not include in the analysis.

##  3 Results

Parameter | Sinusoidal model up to 2012 | Sinusoidal model up to 2019 | Linear drift model up to 2019
---|---|---|---
$\theta_{0}$ | $(62.9\pm 0.8)\leavevmode\nobreak\ \mathrm{\degree}$ | $(63.1\pm 0.8)\leavevmode\nobreak\ \mathrm{\degree}$ | $62.4\pm 0.2\leavevmode\nobreak\ \mathrm{\degree}$
$\beta$ | $(0.4\pm 0.1))\leavevmode\nobreak\ \mathrm{\degree/yr}$ | $(0.5\pm 0.1)\leavevmode\nobreak\ \mathrm{\degree/yr}$ | $0.2\pm 0.2\leavevmode\nobreak\ \mathrm{\degree/yr}$
$A$ | $(6.9\pm 0.8)\leavevmode\nobreak\ \mathrm{\degree}$ | $(6.9\pm 0.8)\leavevmode\nobreak\ \mathrm{\degree}$ | -
$T$ | $(6.7\pm 0.2)\leavevmode\nobreak\ \mathrm{yr}$ | $(6.9\pm 0.2)\leavevmode\nobreak\ \mathrm{yr}$ | -
$1996-t_{0}$ | $-(3.06\pm 0.24)\leavevmode\nobreak\ \mathrm{yr}$ | $(-3.15\pm 0.25)\leavevmode\nobreak\ \mathrm{yr}$ | -
Table 2: Best fit values of the sinusoidal and linear drift model derived from
a $\chi^{2}$ fit to the observed data. First column shows the model parameters
for the different model and data used. The second column shows the best fit
values derived from fitting a sinusoidal model (Equation 1) to the data up to
2012 i.e., the based on data of Martí-Vidal et al. (2011); Alberdi et al.
(2013). The third column shows values derived from the sinusoidal model
including the new data from 2017 and 2019. The third column shows the best
values of linear drift model (Equation 7), including the new data from 2017
and 2019.

In the following sections we proceed by testing the three hypothesis presented
in Martí-Vidal et al. (2011) and Alberdi et al. (2013).

###  3.1 Sinusoidal jet procession

We adapt the model proposed in Martí-Vidal et al. (2011):

$\theta(t)=\theta_{0}+A\cdot\sin\left(\dfrac{2\pi}{T}(t-t_{0})\right)+\beta\cdot(t-t_{0}),$
(1)

where $\theta(t)$ is the position angle as function of time, $\theta_{0}$ is
the initial position angle value at time $1996-t_{0}$, $T$ is the oscillation
period in years and $\beta$ is the linear drift slope in degrees per years. We
extract the measurements presented by Martí-Vidal et al. (2011), and fit the
data up to the year 2012. The second column of Table 2 reports the values
derived in this manner. Figure 1 shows the best fit. The shaded regions show
the $1\sigma$, and $3\sigma$ contours derived by sampling $1000$ model
realizations from the best fit values and corresponding errors, where we
assumed a Gaussian distribution and took into account the covariance of the
best fit values. The model is able to predict the observations in 2017 and
2019 well, with the predicted values within the $3\sigma$ contour. Figure 5
shows the best fit model when the new data is included, the best fit
parameters are reported in the third column of Table 2.

Figure 1: Black dots show the position angle measurement as function of time
up to the year 2012. The orange pentagons show the 5 GHz data derived in this
work. The black line shows the best fit model to the data up to 2012 by
Alberdi et al. (2013), excluding the new measurements, and extrapolated to the
year 2021. The grey shaded region indicates the $1\sigma$ and the $3\sigma$
contours.

Unfortunately, it is not straightforward to determine the uncertainty of the
position angle accuracy. We estimate the uncertainty of each data point by
fitting the evolution of the data by a non-parametric Gaussian process444We
follow the scikit-learn cookbook for Gaussian process regression.. The
uncertainty of the Gaussian process model is then used as a proxy of the
uncertainty of a datum at a given time. This allows us to do a model selection
test against a more simple baseline model: a simple linear drift (Equation 7,
Figure 6). We report the best fit values of this model in the fourth column of
Table 2. The reduced $\chi^{2}$ of the linear drift model is
$\chi^{2}_{\rm{linear}}\approx 38.5$, where as the sinusoidal model has
$\chi^{2}_{\rm{sinusoidal}}\approx 4.5$. The sinusoidal model is favored over
a simple linear drift.

###  3.2 Frequency dependent jet-modulation

Martí-Vidal et al. (2011) reported a sinusoidal modulation of the M81* core
position angle both at $5\leavevmode\nobreak\ \mathrm{GHz}$ as well as at
$1.7\leavevmode\nobreak\ \mathrm{GHz}$ and found a $(1.9\pm
0.4)\leavevmode\nobreak\ \mathrm{yr}$ time lag between the frequency bands.
This was interpreted as differential cork-screw-like precession where the
core-shift effect (Konigl, 1981; Marscher & Travis, 1996) leads to longer
wavelengths probing regions at a larger separation from the black hole. The
model therefore makes a prediction for our higher frequency observation at 8
GHz. Typically a linear relation ($r_{c}\propto\nu^{-1}$) for the core-shift
is found (e.g., Sokolovsky et al., 2011), and we thus expect a similar lag of
$1.9\leavevmode\nobreak\ \mathrm{yr}$ in the 8 GHz observations but in
opposite direction. Figure 2 shows that while the observations are consistent
with the period and amplitude of the oscillation, the data favor a larger time
lag of $\Delta P_{\mathrm{8GHz}}\sim 3.5\leavevmode\nobreak\ \mathrm{yr}$.
This result is driven by the 2019 observation, which suffered from poor data
quality. If one disregards the 2019 data, the observations are consistent with
a shift of $1.9$ years (see Figure 7). This illustrates that the available
data set is insufficient to test this hypothesis, and future observations are
required for a more definitive statement.

Figure 2: Multi-frequency data of the core position angle of M81*. The black
points indicate the $5\rm{GHz}$ position angle as presented by Martí-Vidal et
al. (2011), the orange pentagons show the new 2018 and 2019 measurements. The
black line with gray contours ($1,2,3\sigma)$ shows the best fit to all
$5\rm{GHz}$ data. The brown points show the $1.7\rm{GHz}$ data; the brown line
shows the best fit to the $5\rm{GHz}$ data, shifted by
$1.9\leavevmode\nobreak\ \mathrm{yr}$ as suggested by Martí-Vidal et al.
(2011). The green points show the $8\rm{GHz}$ measurement; the green line
shows the best fit $5\rm{GHz}$ model shifted by $\sim-3.5\leavevmode\nobreak\
\mathrm{yr}$.

###  3.3 No precession-caused flux modulation

Martí-Vidal et al. (2011) proposed that the flare observed in the years 1998 –
2002 was caused by the variable Doppler boosting of the precessing jet as the
viewing angle periodically changes in the direction of the observer (see also
Ros & Pérez-Torres (2012)). The top panel of Figure 3 shows the best fit model
and the position angle measurements. We include the two newest 5 GHz flux
density measurement in the bottom panel. We fit a simple Gaussian + flux
offset model to the flare data. The best fit model is plotted in gray in
Figure 3. If the flare is caused by the precession of the jet, one expects the
re-occurrence of a similar flare shape shifted by the period. We illustrate
this by plotting shifted realizations of the best fit Gaussian flare model,
shifted by multiples of the precession period. It is clear that the low flux
measurements in the years after 2002 are inconsistent with such a scenario.
However, given the sparse sampling of the light curve, it is possible that the
observations miss flaring activity if the correlation to the precession period
is not very tight.

Figure 3: The top: position angle measurements alongside the best fit model
(Equation 1). Lower panel: the 5 GHz light curve of M81*. The black lines
indicate the data extracted from Martí-Vidal et al. (2011); Alberdi et al.
(2013), the orange pentagon denotes our newest measurement. The gray line
shows a best fit Gaussian model which approximates the observed flare. The
vertical line indicates the peak of the Gaussian flare model. The Gaussian
flare shape is shifted by the precession period ($6.9\leavevmode\nobreak\
\mathrm{yr}$).

###  3.4 A precession-nutation model for M81*

Britzen et al. (2018) analyzed the precession and nutation of the resolved jet
components of OJ287. In the following section, we follow their nomenclature in
order to derive the intrinsic time scales of the system from that observed
(projected) precession and nutation. In subsection 3.1, we modeled this
precession as a sinusoidal modulation on top of a linear drift. In the context
of a precession-nutation model, the linear trend describes (in first order of
a Taylor-expansion) the precession and the additional sinusoidal modulation a
nutation term. The model presented in Britzen et al. (2018), which builds on
model introduced by Abraham (2000), has seven parameters given in Table 3.
While some of the older observations resolved the core structure, our prime
observable is the position angle of the core on sky $\eta(t)$. Further, we do
not detect a strong deviation from a linear trend of the core-position angle.
Thus we cannot constrain the periodicity of the jet-precession $P_{p}$
directly, but can only constrain its value from the observed nutation and the
linear trend. We fit the temporal evolution of the position angle using
Equation 8 of Britzen et al. (2018), and refer the reader to Appendix C for
the mathematical details. We determine the posterior parameters of the model
using dynesty (Skilling, 2006; Feroz et al., 2009; Skilling, 2004; Speagle,
2020). Figure 4 shows the posterior distributions of the precession period
$P_{\rm{p}}$, the nutation period $P_{\rm{n}}$, and the precession cone half-
angle $\Omega_{\rm{p}}$. As argued before, the nutation is driving the
sinusoidal modulation of the position angle with a period $P_{\rm{n}}\sim 7$
years, while the linear trend is caused by a large scale precession of the jet
with a largely unconstrained period (i.e., more than $200$ years, and less
than $1800$ years), and the precession cone angle is constrained to be
positive.

Name | Abbreviation | Value
---|---|---
Precession period | $\mathrm{P_{p}}$ | $(807\pm 335)\leavevmode\nobreak\ \mathrm{yr}$
Nutation period | $\mathrm{P_{n}}$ | $(6.6\pm 0.1)\leavevmode\nobreak\ \mathrm{yr}$
Precession cone half-angle | $\mathrm{\Omega_{p}}$ | $(87\pm 32)\degree$
Nutation cone half-angle | $\mathrm{\Omega_{n}}$ | $(\pm 5.3\pm 1.6)\degree$
Line-of-sight angle | $\mathrm{\Phi_{0}}$ | $(12\pm 39)\degree$
Projected jet-cone-axis | $\mathrm{\eta_{0}}$ | $(62\pm 1)\degree$
Reference time | $\mathrm{t_{0}}$ | $(1994.8\pm 0.2)\leavevmode\nobreak\ \mathrm{yr}$
Table 3: Model parameters and derived parameters of the precession-nutation
model, as originally presented in Abraham (2000) and Britzen et al. (2018).
Figure 4: Posterior of the precession period $P_{\rm{p}}$, the nutation period
$P_{\rm{n}}$, as well as the precession cone half-angle $\Omega_{\rm{p}}$.

##  4 Astrophysical origin of precession

Jet precession is observed for many jetted AGNs, and their origin is typically
attributed to either being of purely stochastic nature (i.e., without true
periodicity), induced by disk-instabilities in tilted accretion disks or to be
induced gravitationally by a pace-maker companion. Following the arguments
presented by Vaughan et al. (2016) we cannot rule out a stochastic nature of
the observed modulation in the M81* core region position angle. Nevertheless,
so far, the apparently sinusoidal modulation of the precession angle proposed
by Martí-Vidal et al. (2011) has both withstood the extrapolation to the
future (albeit with a slightly increased linear slope), as well as the
extrapolation to different frequencies (precession in the X band leading the C
band). The latter is, however, not a proof of periodicity, as one would expect
a frequency dependent-lag of the position angle also for a purely stochastic
jet modulation.

Assuming that the observed modulation is truly periodic, two scenarios for its
astrophysical origin may be of importance. For an accretion disc which is not
aligned with the black hole’s spin axis Lense–Thirring precession (Thirring,
1918) induces a nodal precession of test particle orbits. The strength of this
is effect is frequency dependent, and thus results in a precessing warp of the
accretion disk. Fragile et al. (2007) demonstrated that this may lead to a
constant period precession of the disk around the black hole. Such a disk-
precession is thought to be the cause for Type-C Quasi-Periodic-Oscillations
(QPOs) observed in X-ray binaries (e.g., Stella & Vietri, 1998), and can be
used to estimate the black hole mass and spin under certain assumptions (e.g.,
Ingram & Motta, 2014). Building on the simulations by Fragile et al. (2007),
Liska et al. (2018) demonstrated that titled accretion flows are able to
launch jets, and that the jet precession is aligned with precession of the
disk. In this set of simulations the amplitude of the jet precession depends
on the separation from the black hole, dropping from $100\degree$ at a
separation of $R\sim 10R_{g}$ to $\sim 50\degree$ at $100R_{g}$. Further,
Fragile et al. (2007) found an empirical relation between the precession
period of the disk: $T_{p}\sim 0.3(m/M_{\sun})\leavevmode\nobreak\ s$, which
corresponds to roughly $0.2$ years assuming a black hole mass of $2\times
10^{7}M_{\sun}$. Both the amplitude of the oscillation as well as the
precession period are in slight tension with the observed values
($2\Theta_{p}\sim 7\degree$, $P_{p}\sim 7\mathrm{yr}$). Assuming a precession-
nutation model, the amplitude of precession is more similar to the expected
value ($\sim 80\degree$), however the much longer period in this case is even
harder to contextualize. In this simple argumentation we have, however, not
accounted for projection effects, and none of the simulations have been
tailored to M81* (i.e. unknown spin, and accretion-disk tilt), and have
ignored that the disk precession timescales dependent on the initial disk mass
Liu & Melia (2002). We therefore suggest that the Lense-Thirring precession
scenario may well be applicable in the case of M81*.

Finally, a gravitational pacemaker may explain the observed precession of the
M81* position angle. Such a scenario has been found in the binary system SS433
(e.g., Stephenson & Sanduleak, 1977; Clark & Murdin, 1978) where two large
scale precessing jets create a corkscrew like structure. For this system, the
precession is thought to originate from gravitational torque of the donor star
on the accretion disk of a compact object which is either a black hole or a
neutron star (slaved disk model, Roberts, 1974; Waisberg et al., 2019). A
similar scenario has been proposed for OJ 287 and 3C 345, where an orbital
modulation is present both in the light curve as well as the jet components
(Lobanov & Roland, 2005; Britzen et al., 2018). Further Caproni et al. (2013)
found a $12.1\leavevmode\nobreak\ \mathrm{yr}$ precession period in BL
Lacertae. Britzen et al. (2018) found a precession period of $\sim
23\leavevmode\nobreak\ \mathrm{yr}$, on top a much faster $\sim
1\leavevmode\nobreak\ \mathrm{yr}$ nutation period and derived a binary
separation between $0.001\leavevmode\nobreak\
\mathrm{pc}<d<0.1\leavevmode\nobreak\ \mathrm{pc}$. For 3C 345, Lobanov &
Roland (2005) found a precession period of $\sim 10\leavevmode\nobreak\
\mathrm{yr}$ of the position angle, and which exhibited a linear trend, which
is very similar to the behavior of M81* (short $\sim 7\leavevmode\nobreak\
\mathrm{yr}$ nutation period, a linear trend, which we interpret as a long-
period precession of $\sim 800\leavevmode\nobreak\ \mathrm{yr}$).

If we interpret the seven year period inferred as the orbiting period of the
companion object, we can derive the binary semi-major axis as well as the
gravitational binary merger time. An orbiting secondary black hole induces
gravitational torques on the accretion disc, which results in the precessing
motion in the opposite sense to the disc rotation. The precessing motion is
accompanied by the short-term nutation motion caused by the torque of a
similar magnitude. However, the amplitude is smaller than for the precession
by the ratio of the precession and the orbital frequencies. Following Katz et
al. (1982), see also Caproni et al. (2013), the nutation angular frequency is
equal to twice the difference of orbital and precession angular frequencies,

$\omega_{n}=2(\omega_{\rm{orb}}-\omega_{p}),$ (2)

where $\omega_{p}$ is negative because of the opposite sense with respect to
the orbital motion. Using Equation 2, the orbital period can be expressed as

$P_{\rm{orb}}=\dfrac{2P_{n}}{1-2P_{n}/P_{p}}\approx 2P_{n}.$ (3)

The putative SMBHB in M81 has an orbital period of $P_{\rm{orb}}\sim 14$ to
$15$ years for $P_{p}\geq P_{n}$, which seems to be the case based on the
long-term linear drift. The semi-major axis of the binary system can be
estimated from the third Kepler law

$a_{\rm{bin}}\approx 1573\left(\dfrac{M_{\rm{tot}}}{2\times
10^{7}M_{\odot}}\right)^{1/3}\left(\dfrac{P_{\rm{orb}}}{14\leavevmode\nobreak\
\mathrm{yr}}\right)^{2/3}\mathrm{AU},$ (4)

which corresponds to $a_{\rm{bin}}\sim 8000R_{g}$
($R_{g}=GM_{\rm{tot}}/c^{2}$) in gravitational radii if the primary SMBH
dominates the total mass. Using the primary mass fraction of
$x_{p}=m_{1}/M_{\rm{tot}}\sim 0.9$ (the secondary mass fraction is $x_{s}\sim
0.1$), the binary merger timescale is

$\displaystyle\tau_{\rm{merge}}$
$\displaystyle=5/256\dfrac{c^{5}}{G^{3}}\dfrac{a_{\rm{bin}}^{4}}{x_{p}x_{s}M_{\rm{tot}}^{3}}$
(5) $\displaystyle=2.77\left(\dfrac{a_{\rm{bin}}}{1573\leavevmode\nobreak\
\mathrm{AU}}\right)^{4}\left(\dfrac{x_{p}}{0.9}\right)^{-1}\left(\dfrac{x_{s}}{0.1}\right)^{-1}\left(\dfrac{M_{\rm{tot}}}{2\times
10^{7}\leavevmode\nobreak\ \mathrm{M_{\odot}}}\right)^{-3}\leavevmode\nobreak\
\mathrm{Gyr}.$ (6)

For an even more extreme ratio, $x_{p}\sim 1$, $x_{s}\sim 10^{-2}$, we obtain
$\tau_{\rm{merge}}\sim 25\leavevmode\nobreak\ \mathrm{Gyr}$, hence the system
would generally be long-lived.

##  5 Conclusions

We present novel observations of the core region of M81*. Our observations are
consistent with a precession of the jet of this galaxy, which was first
proposed by Martí-Vidal et al. (2011). The jet precession period is roughly 7
years. On top of the precession (amplitude $\sim 7\degree$), the jet exhibits
a small linear drift of roughly $0.5\mathrm{\degree/yr}$. However, we cannot
confirm that the flare observed in the years 1998 to 2002 is connected to the
precession of the jet for instance through Doppler boosting. Our sparse flux
measurements do not show elevated flux through the years 2017 to 2019.
Further, historic data does not show any flaring activity since the end of the
last flare in 2002. We can rule out a self-similar modulation of the light
curve with the period of the modulation. However, the sampling of the light
curve is too spare to definitely rule out any modulation scenario. Thus we
consider it more likely that the flare observed in the years from 1998 to 2002
was not caused by variable Doppler boosting. Our observations are consistent
with either a Lense–Thirring induced precession of the jet, or binary-induced
precession of the jet. It aligns itself with observations of other precessing
jets such as in 3C345 and OJ287, which both show a fast nutation-like
component as well as a slower, but larger amplitude precession-like variation
of the jet position angle. If Lense–Thirring precession is responsible for the
observed jet precession in all three AGN, the underlying coupling of the
accretion disk precession to the jet precession would show a remarkable self-
similar coupling through vastly different accretion regimes. While both 3C 345
and OJ 287 accrete close to their Eddington limit, M81* belongs to the class
of radiatively inefficient accretion flows. This may hint that the jet-physics
responsible for the observed precession in these systems maybe accretion-flow-
rate and accretion-flow-state independent. On the other hand, if a binary
black hole is responsible for the apparent precession, then it may be the
closest super-massive or intermediate mass binary black hole candidate.
However, more data is necessary to finally confirm the precessing nature of
M81*, and in particular the proposed frequency dependent time lag.

###### Acknowledgements.

This publication is part of the M2FINDERS project which has received funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 Research and Innovation Programme (grant agreement No 101018682). J.D.
acknowledge support from NSF AST-2108201, NSF PHY-1903412 and NSF PHY-2206609.
J.D. is supported by a Joint Columbia University/Flatiron Research Fellowship,
research at the Flatiron Institute is supported by the Simons Foundation. MZ
acknowledges the financial support by the GACR EXPRO grant no. GX21-13491X.

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##  Appendix A Best fit model including the newest observation

In this appendix we show the best fit model detailed in the third column of
Table 2, as well as the linear drift model (fourth column of Table 2) defined
as:

$\theta(t)=\beta\cdot(t-t_{0}).$ (7)

Figure 5: Same as Figure 1, but including the 2017 datum in the fit. Figure 6:
Same as Figure 1, but for a linear drift model and including the 2017 and 2019
data in the fit.

##  Appendix B Frequency-dependet shift excluding the 2019 observations

We show the same Figure as Figure 2 in Figure 7, but with a model shifted by
$-1.9$ years instead of $-3.5$ years. This is consistent with the well
determined 2018 8 GHz observation, but inconsistent with the 2019
observations.

Figure 7: Same as Figure 2, but with a -1.9 year shift of the 8 GHz model
instead of -3.5 years.

##  Appendix C Full posterior of the precession nutation model

The full posterior of the precession nutation model is given in Figure 8

Figure 8: Joint posterior of the precession nutation model.

##  Appendix D Maps of observation

Below we plot the maps, best-fit models of the respective C- and X-band
observations. LABEL:fig:c-band shows the C-band data, Figure 10 shows the
X-band data. Table 4 gives an overview of the observation details.

Obs. date | Band | Beam size [mas] | Beam angle [$\degree$] | Clean residual RMS [Jy/beam]
---|---|---|---|---
2017-06-21 | C | $0.902\times 0.86$ | $-65.3$ | $0.0004$
2018-06-10 | X | $0.911\times 0.594$ | $-12$ | $0.0002$
2019-11-04 | C | $1.78\times 1.2$ | $-30.3$ | $0.0003$
2019-11-04 | X | $1.01\times 0.755$ | $-29.1$ | $0.0003$
Table 4: Achieved resolution and beam configuration for the four observations.

Figure 9: Maps of the observations obtained in C-band. The beam size is
indicated by the grey ellipse. Sub-figure (a) shows the C-band observation
obtained with the EVN on June, 2017; sub-figure (b) shows the C-band
observation obtained with the VLBA on November, 2019..

Figure 10: Same as Figure 9, for observations obtained in X-band. The beam
size is indicated by the grey ellipse. Sub-figure (a) shows the X-band
observation obtained with the EVN on June, 2018; sub-figure (b) shows the
X-band observation obtained with the VLBA on November, 2019.

##  Appendix E Participating stations

Table 5 gives the participating stations and their abbreviations.

abbreviation | Observatory name | Location
---|---|---
EF | Effelsberg | Germany
IR | Irbene | Latvia
YS | Yonsei | R. o. Korea
TR | Torun | Poland
SH | Shanghai Astronomical Observatory | P.R. China
MC | Medicina | Italy
WB | Westerbork Synthesis Radio Telescope | the Netherlands
JB | Jodrell Bank Observatory | United Kingdom
BR | Brewster | USA
FD | Fort Davis | USA
HN | Hancock | USA
KP | Kitt Peak | USA
LA | Los Alamos | USA
MK | Mauna Kea | USA
NL | North liberty | USA
OV | Owens Valley | USA
PT | Pie Town | USA
SC | St. Croix | USA
Table 5: Station names, abbreviations and location of the participating EVN
observatories.