about Model for KIC846 Dust Cloud Geometry (not Physical Mechanism Model)
Last July someone e-mailed me a prediction of a brightening
after the series of 2017 dips was over, and mentioned late
September or October for when this should occur. In August he
revised the prediction to a brightening in October. At the time
I didn't understand why he was predicting this, but in September
we began to collaborate on a joining of my HAO observations with
his modeling (he has developed a 2-D transit model for
complicated ring systems, comas and dust clouds that appears to
be more sophisticated than anything published). I now understand
why he was predicting a brightening, and since it is underway we
want to "go public" with this prediction.
I want to present an overview of what we know about the
brightness behavior of KIC 8462852 (hereafter, KIC846). Two very
basic observational facts should be beyond dispute by now:
1) U-shaped fade events of ~ 1 or 2 %,
lasting about a year, occur at 1600-day intervals, and
2) Near the end of the U-shaped fade event a
half dozen short-term dips occur.
If anyone questions the above two "observational facts" I would
like to get an e-mail with the argument (no opinions, please)
for disputing them. As one professional astronomer likes to say:
"Mysterious objects usually can't be understood until they
exhibit periodicity of some sort." Well, the above two
"observational facts" provide a periodicity of sorts! I view
them as a good "starting place" for developing new
understandings, as I present the following (self-evident)
3) Something orbits KIC846 with a
period of ~ 1600 days (ie., at an average distance of 3.0 AU).
4) Things orbit the above object, and their
dust produces the short-term dips. The object being orbited must
be a "massive object."
Because a set of objects can't be in an identical orbit this
close to each other; only the 5 Lagrange regions permit
stability in orbits with the same period.
5) The things that orbit the 1600-day
"massive object" have orbits that extend on each side by "an
orbit circumference fractional amount" = (400 days / 2) /
1600 days = ~ 1/16.
400 days is the length of the "1-year fade feature" (which is
actually closer to 1.2 years).
6) Assuming the objects that orbit the
"massive object" are within the massive object's Hill sphere,
the massive object must have a mass of > 14 ×
Anything more massive than ~ 13 × M_Jupiter is a candidate for
being a brown dwarf (BD); hereafter I'll refer to the "massive
object" as a BD.
7) The dips are produced by dust (that
could be configured as a tail, a coma or a ring system) that
originates from moon-size objects orbiting either the BD or
planets that orbit the BD.
Because the "gravity well" for the BD, or any orbiting planets,
will be too deep! Comets produce dust tails because their
gravity wells are shallow.
Again, if anyone questions the above 5 points, I would like to
hear from you with your argument (no opinions, please).
Let's review some of the photometric evidence for everything
that forces us to the Fact#1 and Fact #2 starting points. (A
fuller development of all of the above will be treated in a
manuscript, in preparation, that I'm working on with two other
authors - one of whom is the person who e-mailed me in July and
September predicting a brightening in September or October). By
the way, if anyone is aware of a professional astronomer
predicting a brightening (and making that prediction before it
began) I would really appreciate hearing about that.
Figure 1.1 shows how my collaborators view what the Kepler
light curve would have looked like if Kepler
had continued beyond Kepler
day 1590. Let's refer to the
2 % fade (starting at "B" in Fig. 1.1 and ending at "D") as a
"U-Shaped Fade Feature," or "drop" for short. We suggest that
the beginning of the "drop" repeated ~ 11 months ago
(2016.11.08). Similarly, we suspect that the group of dips ("C"
in Fig. 1.1) repeated this year, during May to October. If so,
then a brightening should follow this year's group of dips, and
it should start October 2017.
Figure 1.1. Kepler observations, as re-processed and
published by Montet and Simon (2016). We have repeated the
Kepler data (1580 days worth) with a repeat interval of 1800
days in order to illustrate what might have been observed if
Kepler had been able to continue observing KIC846. AAVSO data
in the second "B" region agree with the shape of the repeated
Kepler "drop" fade. (We prefer a repeat interval of
1600 days, but the details of this are still being worked
out.) The letters denote locations of the brown dwarf in its
orbit, shown in the next figure.
The interval between the median activity level of Kepler
short-term dips and this years dip activity is 1584 ± 44 days
(as I described a few days ago on this web page). My
collaborator (he is "shy" and he doesn't want me to use his name
until receiving a positive review of his work) has developed a
model for simulating the transit of complicated ring structures
(many rings, each with their own opacity), comas and dust
clouds. He has applied this model to a configuration consisting
of a brown dwarf (BD) in a 1600-day eccentric orbit. The BD has
a ring system, and in addition at least 3 planets (with moons)
in orbit about it (within the BD's Hill sphere). Every time the
BD and its planets orbit close to KIC846 (periapsis is shortly
after "C" in Fig. 1.1), volatiles and dust are released, just
like what happens to comets in our solar system (note: this idea
is consistent with the KIC846'"snow line"). The BD planets have
moons, and they are the source for the release of volatiles and
dust (note: the moons have a lower escape speed than the planets
they orbit, so volatile-driven dust is able to escape the moons
but not the planets).
Figure 1.2 is the eccentric 1600-day orbit that my colleague has
developed to account for these events (as well as others), to be
described in a forthcoming paper. It's my view that the BD has a
planet and ring system that is the source for dust that escapes
the BD Hill sphere to produce a dust cloud that is responsible
for the 1 or 2 % fade every 1600-day orbit. The cloud is kept
from continually expanding due to light pressure from KIC846.
This implies that dust production is continuous. The "drop"
events last ~ 1 year, and they are followed by a brightening due
to a clean line-of-sight to the star following passage (in
addition, there's a component of brightening due to a change in
geometry of starlight illumination of the dust cloud and rings).
. Brown dwarf eccentric 1600-day orbit that
my colleague has developed to account for the U-shaped "fade"
and short-term dips. The BD has a ring system, as well as a
couple planets with moons that are subject to the release of
volatile molecules and dust (similar to comets) when they are
close to periastron (which is now). The dust cloud is
just one speculation that might account for the U-shaped
"fade" at 1600-day intervals. Another model for the U-shaped
fade is being evaluated, which relies upon changes in geometry
of reflected light off large particles. The increasing orbital
speed may be a factor in producing the ingress/egress
asymmetry of the U-shape.
Here's a more accurate depiction of the orbit that we
suggest can account for the dip patterns.
. Brown dwarf orbit with 3 Kepler day
number locations indicated. Eccentricity ~ 0.5, periastron ~
1.2 AU, apoastron ~ 4.8 AU, period = 1601 days (4.4 years).
[Orbit determined by R. Bourne]
The above orbit predicts radial velocity vs. date, RV(t), shown
in the next figure below.
Figure 1.4a. Predicted RV(t) (blue
symbols), units of km/s, for the F2V star KIC846 on the
assumption that a brown dwarf is in a 1601-day elliptical
orbit (e = 0.5) and with the line of apsides oriented in a way
to account for a series of transit events at the times they
were observed by Kepler in 2013 and ground-based observatories
in 2017. The 4 measurements in 2014 and 2015 were reported in
the discovery paper. The red diamond shows the "now" date.
We've adopted a mass for the brown dwarf near the maximum for
such a star, 70 × M_Jupiter. Since RV(t) is proportional to BD
mass this is an approximate maximum amplitude model. [These
calculations made by R. Bourne]
Figure 1.4b. Same as above, but showing how
the assumed BD mass affects predicted RV(t).
Since the BD is now going away from our solar
system the star KIC846 is approaching at close to the maximum
speed in its 4.4-year orbit. (Since the KIC846 binary system has
an average motion away from our solar system, which is greater
than the orbital speed of the KIC846 star, the previous sentence
could be modified to say that the KIC846 star is predicted by
our model to be receding from our solar system with a minimum
The next figure shows Kepler data (re-analyzed by Montet &
Simon, 2016) and HAO measurements of g'-band (and V-band,
converted to g'-band) for a 9-year interval. The model trace is
a crude representation of an asymmetric U-shaped "fade" with a
shape this is approximately compatible with the Kepler
observations (assuming their overall pattern repeats every 1600
days). The trace is just a mathematical model; a physical model
is now under development for inclusion in a forthcoming paper.
Figure 1.5. Kepler
data (upper panel, as re-analyzed by Montet & Simon,
2016) and HAO
data vs. Kepler Day# (lower panel). A model for
long-term normalized flux that is inspired by
the Kepler data has been created to fit the HAO
data. The U-shaped "fade" that fits HAO data
appears 1600 days later than the U-shaped fade
feature that fits Kepler data. The
model also includes a linear trend between the U-shaped
fades (1600 days apart). The U-shape is asymmetric,
meaning that ingress occurs slowly and egress occurs
rapidly (with "cosine((t-to)/tau)^0.4" shapes for each
half). The current U-shaped fade has a minimum
brightness on 2017.07.06; ingress is at 2016.11.08 and
egress is at 2017.11.09. The OOT brightness is now
approximately half way to a full recovery, according to
this mathematical model.
In Fig. 1.5 notice that whereas the
shape of this year's U-shaped fade is the same as the U-shaped
fade that we claim represents Kepler
data, the depth and
length differ. According to my simple model fit to the current
long-term "drop" fade, its length will be ~ 1.0 years, from
ingress to egress. The previous event, observed by Kepler
lasted at least 1.4 years (observations ended before egress, so
we can only speculate on the length of the U-shaped fade).
Another difference is depth: the current event has a depth of
1.0 % (from ingress to mid), whereas the Kepler
was ~ 2.4 %.
Here's a "zoom" of the lower panel of the previous figure.
Figure 1.6. HAO
g'-magnitude (and V-mag's converted to g'-mag scale) for
the last 1000-day.
We have a draft of a paper that is undergoing "informal" review
by a couple experts in the field, and if they endorse submission
for publication (subject to the usual suggested changes) we will
submit the paper to MNRAS
(we can't afford any journal
with page charges).
If that journal eventually accepts
the paper for publication, after many months of reviewer
negotiations, it will appear in the journal sometime next year
and at arXiv sometime this year. If MNRAS rejects the paper then
it will appear at this web site sometime in November.