WD 1145+017 Observational Findings that Need Modeling
2019.07.10, B. Gary
During the past 3.7 years I've analyzed 354 observing sessions of WD1145, yielding a light curve for each. My 14" and 16" telescopes were used for most of these (61 %). Other contributors are Tom Kaye (19 %), Josch Hambsch (9 %), Roi Alonso (6 %) and Paul Benni (4 %). I have identified 1717 dips in these LCs, all of which have been fit by the AHS function. Statistics for dip depth and width are presented here (Fig. 1 and 2). Waterfall plots of dip location were used to identify 106 drift lines. Their "existence duration" histograms are presented (Fig. 3). Several drift line properties (depth and width) have been studied vs. date; one of them exhibits impressive stability over a 3-month interval (Fig. 4). Drift lines sometimes exhibit a "bend" in slope, and occasionally the bend date is associated with the appearance of new drift lines with a range of slopes (Fig. 5). Activity level, defined as fraction of "missing" flux due to dips, summed over an orbit, change with timescales of a few days and also years (Fig. 6). The activity level during the 2016/17 observing season reached a level that was 100-fold greater than during the Kepler discovery observational dates. Dips with drift lines slopes corresponding to periods close to 3 of the 6 periods found in Kepler data have been observed from follow-up ground-based data. Whereas almost all dips are associated with the A system, several are associated with the next orbit out D system (Fig. 7), and a small number are associated with the 3rd orbit B system. Figure 8 summarize this. Occasionally a set of dips distributed over a large range of orbit phases will undergo a simultaneous increase in activity, as occurred during 2017 January to March, (Fig. 9). When circumstellar gas disk absorption lines are observed during a dust cloud dip event the UV line absorption strength decreases in relation to optical dip depth in a way that requires different projected area on the WD disk for the absorbing gas and dust cloud. The circumstellar gas disk must project a smaller fraction of the WD disk than the larger dust cloud (Xu et al., 2019). Models for projected areas and dust cloud opacity can account for this relationship (Fig. 10), but solution dust cloud is narrow and opaque. The problem with this result is that a dust cloud with an opaque strip along the centerline should produce "flat-bottom" dips on occasion, and none have been observed. This web page's purpose is to summarize the wealth of photometric observational findings obtained so far in order to generate interest by modelers to construct realistic physical models for the specific case of WD1145.  
Categories of Photometry Observational Findings Relevant for Physical Model Development

There are several categories of observational findings that can guide model development. Here are 10 categories.

1) Dip Depth Statistics

Figures 1a and 1b. AHS depth histograms for a sample of 1717 dips reported during the past 4 observing seasons.

Figure 1c and 1d. Histograms for depth for the most active and least active seasons (left) and all four seasons (right). (Disregard the falloff at small depths, which is due to use of small-sized amateur telescopes).

Median dip depth for all seasons is ~ 14 %. Using an amateur 14" telescope dips with depth of < 7 % are under-reported. Based on a simple log/linear plots (Fig. 1b) dips with a depth of 2 %, for example, must be twice as numerous as the 7 % dips (that can be detected reliably).  Dips with depths exceeding ~ 40 % exhibit a different incidence of occurrence vs. depth than applies to the shallower dips (for both seasons when depths exceeding 40 % were present). The deepest dip measured during 4 observing season is ~ 66 %.

Figure 1e. Histogram using uniform intervals for log(depth). Depths < ~ 7 % are under-counted due to SNR limitations of my telescope (14"). The break at 40 % is real and may be related to the inclination of dust cloud orbits that produce a preference for transiting in front of one hemisphere of the WD disk more than the other hemisphere. 

The interpretation extremes are that 1) dust clouds are opaque, with projected areas (and abrupt edges) that cover as much as 2/3 of the WD disk, and 2) dust clouds can cover the entire WD disk with average transparencies < 1/3. Can the slope of the depth histogram in Fig. 1e, in the depth region 7 to 40 %, be used to assess compatibility with collision cascade models?

2) Dip Width Statistics

Figures 2a and 2b. AHS width histograms.

The median dip width, as measured using the AHS function, is 0.077 phase units (FWHM = 0.10 phase units). This is much smaller than would be produced by Keplerian shear of a one-time created dust cloud to spread to larger widths.

Some physical mechanisms have to be continually creating and destroying dust. 
3) Dip Duration Statistics

Figures 3a and 3b. Duration of drift line histograms.

The median duration of dips (that can be identified by their appearance at expected phases for several observing sessions) is > 40 days. This is much longer than the time it takes for Keplerian shear to spread a one-time created dust cloud into something resembling a ring of approximately uniform dust density around the orbit.

Some physical mechanisms have to be continually creating and destroying dust.

4) Dip Properties Stability

Figures 4. Dust cloud width and depth vs. date for a 3-month interval in 2019.

The 30 % depth requires a dust cloud vertical thickness  > 0.5 Rwd (assumes opaque cloud band with zero impact parameter, i.e., extending from 0.25 Rwd below WD center to 0.25 Rwd above). Ejection velocities must be as high as 0.75 km/s (assumes isotropic ejections). This dip's width is stable at ~ 0.05 phase units (FWHM ~ 0.065 phase units, 5% level ~ 0.185 phase units). Keplerian shear for 0.75 km/s is 7.5 Rwd/day, which is 0.012 phase units per day. A total shear of 0.185 phase units (corresponding to the 5 % level of the AHS fit) will occur in 15 days.

Does this dips behavior (30 % depth and size stability of 0.05 phase units, using AHS parameters tau1 + tau2) mean that the farthest away particles (which presumably are the smallest ones that are moving fastest) sublimate to vapor after 1 or 2 weeks? Does the stability of dip depth mean that particles are being produced continually (during collisions every half orbit)?

5) Drift Line Bending Events

Figures 5a. Drift line waterfall plot for the second half of the 2018/19 observing season, using a period for the A-system fragments. Bent drift lines are evident for several dust clouds. The circled symbols are for Dip#1, whose width and depth are plotted in the previous figure. The apparent pattern of drift line divergence from a "drift line divergence date of DOY ~ 73 is treated in the Category 9 section. Note: the horizontal bars are not SE uncertainties; they are the AHS tau1 and tau2 locations (where depth is 65 % of the deepest depth). The uncertainties of the dip center location is much less than the span of the horizontal bars (SE is comparable to the size of the circles for Dip#1).

Figures 5b. Drift line waterfall for the 2016/17 observing season (showing 1/4 of the orbit phase) revealing a bending event, possibly caused by a collision in late 2017 January. (The other drift lines radiating from this "collision" are discussed in the Category 9 section.)

If drift line bends are due to gravitational effects due to close passes of fragments then does this provide a way to estimate a combination of parameter values for number density vs. fragment mass?

6) Activity Level Variations

Figures 6. Activity level (fractional loss of flux during an orbit) for a 6-year interval. There's a 40-fold increase in blocked flux from K2 observing dates to the beginning of ground-based observations in late 2015.

The past 5 years of monitoring activity level suggests that "low activity" (1 year) is less common than "high activity" (4 years). It may be possible to assume that activity level is ~ 3 % most of the time and use this to calculate long-term rates for dust production and asteroid mass loss.

About 2.5 % of WD1145 flux is obscured on average during long-timescales of WD1145's life. This can be used to calculate dust production rate and hence estimate total mass of planetesimals available for disintegration after passing through the red giant phase and becoming a WD.

7) Period Shift to Smaller Values When Activity Level Increases

Figures 7a. The 6 Kepler periods correspond to these distances from the WD shown here (for an assumed WD mass and radius). The symbols represent measured drift line periods.

Figure 7b. Detail of relationship between periods of A-system dust clouds and the K2 A period, presumably associated with the A asteroid (for one observing season).

Does this require that only the hot end of an asteroid releases fragments that later may become active in producing dust clouds? Or could fragments be released at both the L1 and L2 sides and they remain dormant until "viscosity" of a permanent cloud of small fragments (too large for obscuring WD starlight but massive enough to affect orbits of newly-created fragments, think > 1 millimeter) causes orbits of the L2 fragments to shrink to smaller than the parent asteroid? (See last section for details.)

8) Simultaneous Increase of Activity Across Broad Phase Region

Figures 8a. Simultaneous change of activity across large span of orbit azimuths.

Figures 8b. Detail of above plot showing that indeed fades in the previous figure does indeed show a simultaneous change at all phase values within that region starting ~ 2017 Jan 21.

Does this mean that dust clouds extend in radial distance as well as orbital azimuth by large amounts, with densities of mini-fragments that are sufficient to activate dust production by previously "dormant" fragments?

9) Drift Line Diverging Events

Many examples exist for diverging drift lines, starting with the sudden rise of activity level in late 2015. Sometime before the start of the 2015/16 observing season activity level increased dramatically (30-fold, from ~ 0.3 % to ~ 9 % average blockage).

Figure 9a. The first two months of dip drift line locations on a waterfall plot exhibit a diverging pattern that project backwards to a date of approximately late August of 2015. This may be the date of a major collision that started what has become a 3-year time of heightened dip activity level.

Figures 9b & 9c. On 2016 Apr 20 there was a sudden appearance of a pattern of dips following 4 drift lines that lasted ~ 2 weeks. All of these drift lines were sloped in a way corresponding to a shorter period than the K2 A-period (labeled "Asteroid"). 

Figures 9d. Drift line waterfall plot using a D system period, showing the dust cloud results of a collision at DOY 415.5. The main fragment revealed itself before the collision, at DOY = 408.2, by a LC with two narrow dips separated by 4.552 +/- 0.001 hours (which was used for establishing the period of this plot). All green drift lines belong to the D-system; the steeply sloped blue and red lines belong to the A-system.

Figures 9e.
Drift line waterfall for the 2016/17 observing season (showing 1/4 of the orbit phase) revealing a possible collision and in late 2017 January. The "main object" has a bend in drift line slope at the collision date and as many as 4 new drift lines diverge with different slopes from that date.

Figure 9f. The most recent drift live divergent event began in early March, 2019 (DOY ~ 72). Notice that there are no dips at this phase before this suggested collision date.

Does this mean that collisions between similar-size fragments initiate dust cloud production (with velocities of up to 1 or 3 km/s)?

10) Relationship Between Gas Disk Absorption Strength and Optical Transit Depth

Figures 10a. Solving for geometry of dust clouds in relation to location of "circumstellar gas disk" for the case of optically thick dust clouds.

[in progress]
Figures 10b. Solving for geometry of dust clouds in relation to location of "circumstellar gas disk" for the case of optically thin dust clouds.
If dust clouds typically have high optical depth they must be located near the WD equator and be narrow in vertical thickness. If they are optically thin then they must extend across much more of the WD disk. .

Sample Format for Physical Model Description

Here's an example of what I think a physical model description might resemble.

There are 6 asteroids with Kepler periods A to F that are in orbits that have shrunk to their WD's Roche radius. Their rotation and revolution are synchronous, causing the WD sub-solar "hot pole" to be hotter than the sublimation temperature of some minerals. Depressions are a few 100 K hotter than surrounding flat surfaces, and the heat wave penetration at these locations causes isolated pockets of sublimation-driven ejection of overlying rock fragments and regolith. Even small ejection velocities will cause material to "drift away" into new orbits because the Hill sphere's surface is close to the asteroid surface. The opposite side will be a "cold pole" and will not experience sublimation jets; for this reason there will be far fewer fragments drifting away from the L2 "cold pole" location into orbits larger than the asteroid's orbit compared with the number of fragments drifting away from the L1 "hot pole" location into orbits smaller than the asteroid's orbit. 

The large number density of fragments in orbits adjacent to and inside the asteroid's orbit mean that large fragments sometimes collide. If the collision debris is ejected isotropically from the collision site all debris particles and sub-fragments will be in orbits that have three components: 1) ejected up or down (inclined orbits with unchanged period), 2) ejected in or out from the WD (eccentric orbits in same orbit plane and same period), and 3) ejected forward or backward along the orbit (same orbit plane but different periods). All debris will be in orbits that come together twice per orbit, at the collision site and anti-collision site - at least for the first few orbits. This can initiate a cascade of collisions every half orbit. After a few orbits the "along orbit" category of debris will spread out along the orbit due to their different periods.

A collision will cause small particles to be ejected at higher speeds than the large particles, rocks and sub-fragments. The smallest particles (< 0.5 micron radius) will sublimate out of existence due to their smallness (emissivity for thermal IR wavelengths is low due to thermal IR wavelength being large in relation to circumference while Bond albedo is unaffected by size since WD radiation is at wavelengths smaller than circumference). This will cause the outer edges of the cloud to disappear after however long it takes for the smallest particles to "overheat" - perhaps a few orbits or days. The cascade of collisions every half orbit will replenish the cloud of debris with a fresh supply and lead to a steady-state dust cloud size.

There are three size categories to consider: 1) radius < 0.5 micron, 2) 0.5 micron < radius < 300 micron, and 3) radius > 300 micron. The smallest particles will be short-lived, most of the light blocking capability will be with the middle size particles and most of the mass and collision activity will reside with the largest size particles.

There's another potential role for the largest size particles, at least the small size end of their size range: they can provide a cloud of particles that provide "viscous drag" for the other particles. Consider those large size particles that are ejected in the orbital direction (fore/aft particles). Those that went behind ("aft" particles) will be in shorter period orbits than those that went ahead ("fore" particles). This means that the other particles (the up/down and in/out particles) will encounter the slower moving "aft" particles (when they are at apoastron) more often than the faster moving "fore" particles (when they're at periastron). Since the slow particles will be encountered more often than the fast particles, the net effect will be to remove orbital angular momentum from the "up/down" and "in/out" particles, which will cause their orbits to gradually shrink.

When the "viscous drag" by fore/aft particles cause the other particles to come closer to the WD, their temperature will increase and they will sublimate out of existence. With additional orbit shrinkage, and increased heat, the minerals will separate into elements. This disk of gas could extend inward from about 40 Rwd. Gas closer than ~ 10 Rwd is removed by some unknown mechanism for deposition onto the WD atmosphere (magnetic field?).

The above is merely an example of what a physical model description overview would look like. Since it's constructed by an "observationalist" it should not be taken seriously.

I hope modelers will become interested enough to take on the challenge of tailoring their model ideas to the WD1145 situation, which is the purpose for this web page.
Related Web Site Links

Details for 2018/19 observing season (data exchange files for all seasons; 1-line description for every image)
Details for 2017/18 observing season
Details for 2016/17 observing season
Details for 2015/16a and 2015/16b observing season
Model speculations (based on early GB photometry observations)

My Collaboration Policy

Please don't ask me to co-author a paper! At my age of 80 I'm entitled to have fun and avoid work. Observing and figuring things out is fun; writing papers is work.

All of my WD1145 observations
are in "the public domain" (as well as my analyses of image sets by observers who have agreed to share their data with me). If any of this is essential to a publication just mention this in the Acknowledgement section.


WebMaster:   Nothing on this web page is copyrighted. This site opened:  2019 June 17