& Summary of Results for this Observing Season:
now have ground-based observations for dips associated with
the A, B and D asteroids (i.e., from 2015 to 2019). On 2019.02.12 a D dip was
observed twice during one observing session; this LC is
used to create an accurate D ephemeris for use with a
waterfall plot for monitoring D dip activity. Several D
dips were later observed with waterfall drift lines that
converge backward in time to a "creation date" of
2019.02.19. At this time just one dip is present. On
2019.03.01 T.Kaye and I observed a very short duration
dip (113 seconds, apparent FWHM), which was broader 3
Full moon 34 degrees away, so noisy.
Figure 2a. "Activity level" for past 4 years.
level" for the past 1.5 years.
Figure 2c. "Activity level"
for the present observing season.
Figure 3a. Drift line plot
for seasons 2017/18 and some of 2018/19. The red lines
have the same ephemeris (period and BJDo).
line plot for the present observing season. (I don't
believe all of the dotted lines either!) DOY 390
corresponds to 2019.01.25, when it appears that the
dust cloud associated with the red drift line
generated two additional fragments that became
active in producing dust clouds. The steeply sloped
green drift line has the D asteroid ephemeris period
Figure 4. D-fragment
ephemeris, showing at least one dip "belonging" to
this ephemeris (at phase 0.50). Perhaps 6 other dips
also belong to the D-fragment period.
Full moon was ~ 34 deg away, causing high noise level.
219.03.15 - TK32
This is an average of data from 3 telescopes.
219.03.15 - TG16
After averaging in groups of 3.
2019.03.15 - BG
2019.03.14 - BG
2019.03.09 - TK
2019.03.09. - BG
2019.03.04 - TK
Averaging groups of 5 (after sorting all observations of this
date by phase).
Averaging groups of 3 (after
sorting all observations of this date by phase).
No averagin (a symbol for each image). Both data sets show a
brightening at phase 0.11. Could this be forward scattering from
a dust cloud that doesn't block the WD disk?
2019.03.04 - BG
2019.03.01 - TK
2019.03.01 - BG
2019.02.28 - BG
Dip #1 has changed shape since the day before: ingress is brief
and egress is slow. One of the group of 3 D dips has disappeared
(the middle one). Of these 6 dips 3 are produced by A fragment
and 3 are produced by D fragments.
2019.02.26 - TK
2019.02.26 - BG
2019.02.25 - TK
2019.02.24 - TK
2019.02.24 - BG
2019.02.23 - BG
I'm not saying the dip at phase 0.56 is the D dip, first seen
on Feb 12, because it may just be a coincidence that it is
located where we were looking for it.
A gibbous moon (81 % illuminated) was 30 degrees away, which
decreased SNR significantly. The first and last dips are 4.55
2019.02.18 - TK
A cleaned-up version.
2019.02.18 - BG
2019.02.17 - TK
2019.02.17 - BG
2019.02.16 - BG
I was "desperate" to observe that D dip, but cloudiness ruined
2019.02.12 - TK
Using the Kepler D period = 4.5500 hrs (and an arbitrary
BJD_ref) this date's phase-folded LC for both HAO and TK16 data,
shows the D dip stable in phase, at 0.79.
2019.02.12 - BG
On this date a "sharp" dip was first seen that belongs to the
D-fragment orbit. During one LC the dip appeare twice, with a
separation o 4.552 +/- 0.004 hours.
This analysis shows that with an exposure time of 60 seconds,
and a cadence of 71 seconds, the actual dip depth (assuming it's
the same for the first and second appearance) is slightly deeper
than the solution based on measurements. A source function with
a deeper depth was convolved with a rectangular exposure
function at appropriate exposure start times, and these results
are shown by the red dash symbols. The source function has a
depth of 25 % (vs. the 23 % that fits the measurements). There
is negligible affect on the apparent width of the dip caused by
a finite exposure time.
This is the AHS model fit when the measured values are fitted
(using sum chi-squares), using one depth and shape with a UT
offset for the second appearance of the dip following the first
appearance by 4.552 hours (also solved-for).
Using the Kepler D period =
4.5500 hrs (and an arbitrary BJD_ref) this date's
phase-folded LC for HAO data shows the D dip stable in
phase, at 0.79. (I later refined the D dips period to be
Phase folding with the A-fragment period shows the main dips at
The more accurate separation of the two main dips is 4.552 +/-
This is the LC that forced me to recognize that a D dip was
present, and it was "sharp" (like most dips at "turn-on").
2019.02.07 - TK
2019.02.07 - BG
2019.02.02 - TK
2019.01.28 - TK
2019.01.27 - TK
2019.01.27 - BG
2019.01.20 - TK
2019.01.19 - TK
2019.01.19 - BG
2019.01.17 - TK
This was a short test observation meant for checking
master calibration files, but it's somewhat useful for
excluding presence of dips.
2019.01.15 - TK
We are puzzled about the main dip being shallower in this
(TK) data than BG data.
2019.01.15 - BG
Note: There is no evidence of the "double-dip" feature that
was present on Jan 12.
2019.01.12 - TK
First observations with TK's new 15" telescope. No
calibration (dark or flat).
2019.01.12 - BG
Dew formed on my front corrector plate, starting (probably) ~
This dip is credible.
I'm skeptical about the two dips at the beginning.
This is the first observation of the season.
Imageand Basic Info
RA/DE = 11:48:33.6, +01:28:29. Observing season centered on
V-mag = 17.2, B-V = -0.08 +/- 0.04, spectral type = DBAZ
Distance from Earth = 142 parsecs (Izquierdo
et al., 2018)
WD mass =
0.63 ± 0.05 x Earth mass =
1.19e30 kg (Izquierdo et al., 2018)
WD radius =
1.32 ± 0.07 x Earth =
8419 km (Izquierdo et al., 2018)
WD Teff = 15,020 ±
520 K (Izquierdo et al., 2018)
A asteroid radius and mass = ~ 200 km and 1/10 Ceres,
i.e., ~ 1020 kg (Rappaport et al., 2016)
Kepler-based transit periodicities (A - F) = 4.49 to
4.86 hours, (Vanderburg et al., 2015)
Asteroid orbital speed (A - F) = 319 to 311 km/s
A asteroid time to cross WD diameter = 53 seconds (for
A asteroid transit depth ~ 0.56 mmag (assuming 200 km
WD1145 (blue circle) is at 11:48:33.59 +01:28:59.3 (J2000).
Red-circled stars have stability suitable for use as
reference. FOV = 27 x 18 'arc, northeast at upper left.
Analyses and Speculations
So far ground-based observations have detected dust clouds
with orbits associated with the K2 measurements of the A, D and
B periods, as shown below.
Figure M01. Scatter plot for some of the drift
lins of the past few years, converted to average orbit
Figure M02. Same data for just the inner-most
three orbits. The WD radius ~ 8400 km, so the A dust clouds
are typically ~ 700 km closer to the WD than their parent
The above two graphs are based on plots like the following:
Figure M03.Waterfall plot for the 2017/18 observing
season, using the A ephemeris (as described in Rappaport,
plot for the current observing season, using the A
ephemeris (as described in Rappaport, 2018).
plot for the current observing season, using the D
ephemeris (described below)
This waterfall plot has evidence for the creation of several
fragments of the D asteroid on DOY 416 (2019 Feb 19).
The use of P = 4.552 hours is required by the 2019 Feb 12 light
Figure M06.This standard light curve shows two
"sharp" dips with identical shapes that are separated by 4.552
+/- 0.004 hours, which corresponds to the K2 D period (4.550
Figure M07.Detail of the first and second
appearance of a dip with identical structure on 2019 Feb 12(shown in previous figure) separated by 4.552 +/- 0.004
hours. The times of image exposures is shown by the x-location
of the red bars, and the average of a hypothetical source
function normalized flux during these exposure times is shown
by the red bar y-locations. The source function was adjusted
to achieve agreement with the observations.
This detail of the two dips shows that the 60-sec exposure times
had only a slight effect on inferred depth of the "source
function" (what would have been observed with short exposures).
The source function has a depth of 25 %. How can a dust cloud
that covers 25 % of the WD disk cross in only 2.5 minutes,
considering that a point source crosses the disk in only 0.9
minutes? This deserves an analysis of the geometry of cloud size
and crossing time.
Let's tell a story describing what may have happened in the D
orbit last week.
where Roche lobe surface has shrunk to coincide with the
asteroid's surface as the asteroid orbit shrinks, vs.
distance from WD1145, for a suite of asteroid densities.
The gravitational field at a distance of ~ 100 x WD radius is
strong enough to synchronize an asteroid's rotation with its
orbital motion. The surface of the Hill sphere (Roche sphere) is
where WD and asteroid D have equal gravity (in a rotating
coordinate system), and it will be approximately coincident with
the D asteroid's surface if the asteroid's density is ~ 3.2
[gm/cm^3], as shown in the above graph.
If the D asteroid has a density of ~ 3.2 [gm/cm^3]
it will be at risk of losing dust and fragments on its
surface when the smallest of ejection velocity outward is imparted
to the dust or fragment. In other words, there is no "escape
velocity" for such an asteroid, and the smallest nudge will send
surface material "floating" away from the asteroid. This
suggestion was made by Rappaport (2016) as a means for producing
a population of fragments in orbits interior to the asteroid.
The reason only interior orbits will be populated is that
fragments will more likely be ejected from the hot pole, the end
of the asteroid facing the WD, than from any other surface
location. (Note: the WD gravity field radial gradients are so
great at 100 WD radii that any asteroids at this distance will
be rotating synchronously with their orbital period.) The reason
for regarding the hot pole as the only source for fragments is
related to the fact that the hot pole will have a heat wave
penetrating the asteroid surface starting with a surface
temperature of ~ 1400 K, whereas the asteroid sides and opposite
pole will be much colder. When the heat wave encounters a layer
with volatile minerals the sublimation of solid to gas can
create a cavity with pressurized gas that will eventually
overcome the structural strength of overlying material and eject
the that material outward.
After this outward ejection of material, or fragment, a fresh
surface is exposed at two places: on the asteroid and one side
of the fragment. Both will initially be colder than the 1700 K
steady-state surface temperature, but they will begin to heat
and produce a "heat wave" that penetrates underlying material.
After the surface of each body reaches 1700 K they may "turn on"
the sublimation process at some level where the most volatile
mineral resides. The timing of when fragment dust clouds are
produced should depend on the rotation state of the fragment. If
it rotates fast the the steady-state surface temperature will be
lower than if it isn't rotating. Assuming the fragment achieves
synchronous rotation it will become hotter on the star-facing
end, and this is where dust production should occur. There are
several factors that can influence activity fragment level, such
as the time to achieve synchronous rotation, but also fragment
shape. It is well known that the bottom of moon craters are
hotter than flat surfaces, due to crater bottoms having a
smaller than hemisphere for radiating away heat. The same thing
can exist on the asteroid and its fragments. I have estimated
that 1900 K is possible, using the moon example. Crater bottoms
may therefore be favored locations for the ejection of dust, or
Here's a repeat of the
waterfall plot using the D ephemeris that was established by
the two dips analyzed in the previous two figures.
Repeat of Fig. M05.
In the above figure let's imagine that the D
asteroid has a large crater that has reached a surface
temperature of ~ 1900 K. Near surface sublimation occurred and
produced a small dust cloud at DOY 408. Since its source is the
asteroid it will have a center of activity fixed to the asteroid
period, not a period associated with an orbit at the asteroid's
front surface. The asteroid's front surface may be 100 km closer
to the WD than the asteroid center, This is indicated by the
first vertical green bar.
This activity subsided by DOY 413, shich accounts for a gap
between the vertical green bars. A subsurface heat wave reaches
lower levels that exceed the temperature of a layer with
volatile mineral, causing the formation of a gas chamber with
pressures that eventually exceed the strength of overlying
material. An explosive ejection of four fragments occurs on DOY
416. Since it was a crater on the star-facing surface that was
the source of the explosive ejection the ejected fragments will
be in elliptic orbits with a smaller average orbit radius than
the parent asteroid. None of the ejection velocity is lost by
overcoming the asteroid's gravity because the WD gravity field
matches the asteroid's gravity (in a rotating reference frame).
This is equivalent to stating that the Hill sphere radius (same
as Roche lobe) equals the asteroid radius. In theory, a rock on
the surface could "float away" with the smallest nudge.
After 4 or 5 days these fragments became active sublimators on
their fresh surfaces, producing the 3 or 4 drift lines sloping
off to the left.
Please don't ask me to co-author a paper! At my age of
almost 80 I'm entitled to have fun and avoid work. Observing and
figuring things out is fun. Writing papers is work. Besides,
most people really don't care about what others have done.
(Google "WD 1145+017" and among the several pages of lame links
none point to my web pages.)
My light curve observations will be "in the public domain" for
this observing season (2017/18). This includes a download of all
LC observations, which I invite anyone to use. If my data is
essential to any publication just mention this in the
acknowledgement section (no co-authorship, please).
Data Exchange Files
Data exchange files are available in two formats: light curve
details (normalized flux for each image) and dip statistics
(asymmetric hypersecant model fits for each dip). The first of
these is available for download here, but I recommend that
anyone using these data check with me for updates (since I
sometimes find errors and post the corrected files here). Data
exchange files of the second format (dip stat's) will be
available here in due time.
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Tom Kaye presentation at 2016 Society for
Astronomical Science meeting: link