6. White Dwarf WD 1145+017 Photometric Monitoring Observations by Amateur Observers B. Gary & T. Kaye
B. L. Gary, this is the 6th of 6 web pages. Last updated 2019.07.10 22 UT

1 of 7 - 2015.11.01 to 2016.01.21:  LC Observations  - 1st  set of LCs, for 2015/16 observing season   
2 of 7 - 2016.01.17 to 2016.07.13:  LC Observations  - 2nd set of LCs, for 2015/16 observing season    
3 of 7 - 2015.11.01 to 2016.07.13:  LC Observations  - 3rd set of LCs, for 2015/16 observing season  (N = 158) + Overview, Results & Model Speculations 
4 of 7 - 2016.10.25 to 2017.06.18:  LC Observations  - 4th set of LCs, for 2016/17 observing season 
5 of 7 - 2017.10.23 to 2018.06.18:  LC Observations  - 5th set of LCs, for 2017/18 observing season 
6 of 7 - 2018.11.06 to 2018.06.15   LC Observations  - 6th set of LCs, for 2018/19 observing season   (YOU ARE HERE)
7 of 7 - All 4 observing seasons: Observational findings that need to be explained by models

Links on this web page:

  Status & Summary of Results for this Observing Season  
  Observing session LCs 
  Finder image & basic info  
  Miscellaneous analysis and speculation  
  Collision model thoughts   
  Data exchange files (for all years: 2015/16, 2016/17, etc)
  My collaboration policy 
  References & related external links 

Status & Summary of Results for this Observing Season: 

The following sequence of phase-folded light curves can be used to study the recent evolution of all dip activity.









The following 3 waterfall plots show dip phase using an ephemeris for the A-fragments.









The following 3 waterfall plots show dip phase using an ephemeris for the D-fragments.







The next 3 lots show dust production "activity" level vs. date.







List of observing sessions   

2019.07.09 - BG16  
2019.07.05 - BG16  
2019.07.04 - BG16 
2019.06.24 - BG16  
2019.06.21 - BG16  
2019.06.20 - BG16
2019.06.19 - BG16  
2019.06.18 - BG16  
2019.06.16 - BG16  
2019.06.15 - BG16  
2019.06.13 - BG16  
2019.06.09 - BG16  
2019.06.06 - BG16  
2019.06.05 - BG16  
2019.05.30 - BG16 
2019.05.29 - BG16  
2019.05.28 - BG16  
2019.05.27 - BG16 
2019.05.26 - TK16 
2019.05.26 - BG16  
2019.05.24 - BG16 
2019.05.21 - BG16  
2019.05.18 - BG16  
2019.05.12 - BG16  
2019.05.11 - BG16  
2019.05.08 - BG16  
2019.05.05 - BG16  
2019.05.04 - TK16  
2019.05.02 - BG16  
2019.04.28 - BG16  
2019.04.25 - BG16  
2019.04.24 - BG16 
2019.04.23 - BG16 
2019.04.21 - TK16
2019.04.21 - BG16
2019.04.13 - BG14  
2019.04.11 - BG14  
2019.04.09 - BG14 
2019.04.08 - BG14  
2019.04.03 - TK32 
2019.04.03 - TK16 
2019.04.03 - BG15  
2019.04.02 - TK16  
2019.03.29 - TK32 
2019.03.29 - TK16 
2019.03.29 - BG14 
2019.03.24 - BG14 
2019.03.23 - BG14
2019.03.15 - TK32 
2019.03.15 - TK16 
2019.03.15 - BG  
2019.03.14 - BG 
2019.03.09 - TK 
2019.03.09 - BG 
2019.03.04 - TK 
2019.03.04 - BG
2019.03.01 - TK 
2019.03.01 - BG 
2019.02.28 - BG 
2016.02.26 - TK  
2019.02.26 - BG  
2019.02.25 - TK 
2019.02.24 - TK 
2019.02.24 - BG 
2019.02.23 - BG  
2019.02.18 - TK 
2019.02.18 - BG 
2019.02.17 - TK 
2019.02.17 - BG 
2019.02.16 - BG 
2019.02.12 - TK 
2019.02.12 - BG 
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 
2019.01.15 - TK
2019.01.15 - BG 
2019.01.12 - TK
2019.01.12 - BG  
2019.01.04 - BG 
2018.12.19 - BG 
2018.12.10 - BG  
2018.12.09 - BG  
2018.12.04 - BG   
2018.11.27 - BG    
2018.11.16 - BG
2018.11.09 - BG  

Observing Sessions  

2019.07.09 - BG16  

Moon 13 degrees away, so noisy! Also, all high air mass.





2019.07.05 - BG16  



2019.07.04 - BG16  

Windy, so noisy.





2019.06.24 - BG16  


Dip labeled "3" is the DIp#1 in the waterfall plot for the A system.






2019.06.21 - BG16  







2019.06.20 - BG16  







2019.06.19 - BG16  







2019.06.18 - BG16  






2019.06.16 - BG16  

Poor data quality (wind), but available if desperate.

2019.06.15 - BG16  







2019.06.13 - BG16





2019.06.09 - BG16  







2019.06.06 - BG16  







2019.06.05 - BG16  





2019.05.30 - BG16  







2019.05.29 - BG16  







2019.05.28 - BG16







2019.05.27 - BG16   







2019.05.26 - TK16  





2019.05.26 - BG16  





2019.05.24 - BG16  







2019.05.21 - BG16  









2019.05.18 - BG16  

Nearby full moon increased noise level.









2019.05.12 - BG16  

Clouds before and after a short clearing provided ~ 1/2 orbit coverage. But it can be combined with data from the night before to provide ~ a full orbit of coverage.









2019.05.11 - BG16  

Clouds before and after a short clearing provided < 1 orbit coverage.



2019.05.08 - BG16  









2019.05.05 - BG16  





2019.05.04 - TK16  







2019.05.02 - BG16  









2019.04.28 - BG16     









2019.04.25 - BG16  









2019.04.24 - BG16 








Notice several events of cloud losses, as much as 1.5 mag's. 

2019.04.23 - BG16 

This is the second observation with my new telescope. It's short because I'm calibrating other properties of the hardware, but the data indicates that quality is improved over what my Meade 14" provided.





2019.04.21 - TK16 

Warm WX, and darks not at same temp as lights so cal did poor job.









2019.04.21 - BG16 

This is the first LC I made with a new telescope, an Astro-Tech 16" Ritchey-Chretien.








This is the first LC made with a new telescope, an Astro-Tech 16" Ritchey-Chretien. It was windy most of the night, so data quality suffered.

2019.04.13 - BG14  









2019.04.11 - BG14 









2019.04.09 - BG14  









2019.04.08 - BG14  









2019.04.03 - TK32 



2019.04.03 - TK16  











2019.04.03 - BG14  








Wind degraded several images. A few clouds were also present.

2019.04.02 - TK16 









2019.03.29 - TK32


9 % outliers removed.

 


This LC has 9 % outliers removed.







 


2019.03.29 - TK16 







2019.03.29 - BG14 







2019.03.24 - BG14









2019.03.23 - BG

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 hours apart.

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 my observations.





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 4.552 hrs.)


Phase folding with the A-fragment period shows the main dips at different phases.


The more accurate separation of the two main dips is 4.552 +/- 0.004 hours.


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) ~ 9 UT.

2019.01.04  





2018.12.19 





2018.12.13





2018.12.10  




This dip is credible.

2018.12.09 


I'm skeptical about the two dips at the beginning.

2018.12.04



2018.11.27


 

2018.11.16



2018.11.09 


This is the first observation of the season.


Finder Image and Basic Info

RA/DE = 11:48:33.6, +01:28:29. Observing season centered on March 16
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 central crossing)
A asteroid transit depth ~ 0.56 mmag (assuming 200 km radius)


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.

Miscellaneous 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 radius. 



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 asteroid.


Figure M03. Diagram, to scale, of the Kepler A, D and B orbits, looking "down" from a "pole", including the 2015/16 dips associated with the Kepler A period, located at random orbit asimuths but at their true orbit distances. The shape, labeled "Most common dip size," corresponds to a dip size that produces a dip depth of 30 % (which was comon for that season). Since particles ejected with velocity components for and aft are orbitally sheared to greater and smaller azimuth values they define an oval shape that would keep expanding if those particles didn't sublimate out of existence.   

The above two graphs are based on plots like the following:


Figure M04. Waterfall plot for the 2017/18 observing season, using the A ephemeris (as described in Rappaport, 2018).


Figure M05. Waterfall plot for the current observing season, using the A ephemeris (as described in Rappaport, 2018).


Figure M06. Waterfall 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 curve, below.


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 hours).



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.

Speculation:

Let's tell a story describing what may have happened in the D orbit last week.


Figure M08. Distance 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 additional fragments.

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.

COLLISION MODEL

The paper by Su, Jackson & 15 others (download) presents a model that can account for observed variations of near-IR thermal emission of a young star's debris disk. The model is based on collisions that produce dust clouds with finite lifetimes, and I think it has possible use in explaining WD1145 transit fades. Although the paper's purpose is to account for IR thermal emission from the debris disk the same dust cloud model could be used to explain transit dips of the star by such a disk if it was inclined edge-on.

The WD1145 discovery paper (Vanderburg et al, 2015) suggested that the transiting dust clouds are produced by the sublimation of minerals on the surface of planetesimals (in the 5 Kepler orbits). Presumably, a mineral molecule would sublimate from the surface and combine with others to form a particle, and this particle would continue to move away from the surface to join other such particles and form a cloud. I personally preferred a model in which a heat wave penetrated to a depth where a volatile mineral was present, and when it sublimated the gas pressure build-up until it overcame structural forces of overlying material and explosively created a jet that ejected the overlying particles. (From my moon work, 5 decades ago, I knew that depressions were warmer than a surrounding flat surface, and these depressions were favored sites for the creation of "sublimation jets." Observations by the Rosetta spacecraft, orbiting Comet 67P, found dramatic evidence for this with deep pits being the source for ejected material.) Ever since this model was under consideration there has been no credible mechanism to account for the large ejection velocities required for the particles in such clouds. Note that this model assumes quasi-continuous production of dust due to either surface sublimation or sublimation jets that eject overlying dust. Whereas the discovery paper assumed the source of these dust ejections was a planetesimal (on of the 5 associated with periods A through F), later thinking favored dust coming from a source of many fragments that drift away from the planetesimal (due to Hill sphere shrinking to the planetesimal's surface). Each dust particle would have an ejection location that its new orbit would pass through. Although it is likely that particles are ejected isotropically, with a range of speeds, it will be useful to focus attention of the following 3 velocity components: up/down, in/out and fore/aft.

Particles ejected
vertically (up/down) would be in inclined orbits. Their maximum vertical extent would be determined by the ejection speed; their orbital period would be unchanged. The particle would pass through the fragment's orbit plane (and close to the fragment) twice per orbit: once at the ejection location and once at the opposite orbit location.

Particles ejected in a radial direction (in or out), either toward the WD or away from it, would be in eccentric orbits confined to the fragment's orbit plane; their orbital period would also be unchanged. The maximum radial extent of the motion of these particles would also depend on the ejection velocity. These particles would return to their ejection location twice per orbit: at the ejection location and the opposite orbit location.

Particles ejected parallel to the fragment's orbit motion, either
forward and backward in direction (for/aft), would be in eccentric orbits with different periods. Those ejected forward would have their periastron at the ejection location and those ejected backward would have their apoastron at the ejection site. Because these fore/aft ejections lead to different orbit periods these particles would undergo "orbit shear," also referred to as "Keplerian shear." As time passes they would spread out along the orbit in both directions.

Let's summarize the properties of the three ejection components:

1) up/down: Same P. Vertical range (above & below original orbit plane) determined by ejection speed. All up/down particles come together twice per orbit.
2) in/out:     Same P. Distance outward/inward from original orbit determined by ejection speed. 
All in/out particles come together twice per orbit.
3) fore/aft:  Different P. Range of periods depends on ejection speed range. Particles continue to spread out along the orbit to distances proportion to time since ejection.

The ejection velocity vector for a typical particle (assuming isotropic) will have components for each of the three directions. The particle can therefore be expected to return to the ejection location, and anti-ejection orbit locations, every orbit, and during subsequent orbits slowly spread out along the orbit either ahead or behind the source fragment.
Even particles belonging to the first two categories will eventually move away from the source fragment due to radiation pressure, collisions, charge accumulation and interactions with other charged particles and Poynting-Robertson drag.
 
So far there is nothing exotic about the above scenario; the big problem is that sublimation jets are thought to be incapable of ejection velocities needed to account for the observed dust cloud sizes. Dips are typically 4 minutes in duration, which corresponds to a size that is ~ 5 times the WD disk diameter. We've observed dip depths of > 60% on a few occasions. If the dust clouds are opaque (with abrupt edges) then we can consider them to have the shape of a band that's long in the orbit direction, and narrow vertically, as it transits the WD disk. If the obstructing dust cloud is a band that crosses disk center, then to produce a 60 % blockage the vertical width of the dust cloud would have to be 0.50 x WD diameter. This would require that some particles are in orbits
inclined so that they extend to the + and - 0.50 WD radius locations. For particles to reach those heights above the source fragment's orbit plane they would have to be ejected with a speed of 2 km/s (as derived below). So far no one has made a case for sublimation jets being able to achieve these speeds.

Collisions, on the other hand, can achieve speeds of these amounts [need a reference for this]. Whether a particle is ejected by a sublimation jet or a collision, it will be subject to the same celestial mechanics described above. A particle ejected from a collision will have the same behaviors associated with the up/down, in/out and fore/aft categories. The up/down and in/out particles would be in orbits that return them to the collision location, and anti-collision location, every orbit. The fore/aft particles would initially join the other particles for these convergences, but over time they would spread out along the orbit. In other words, the dust cloud would expand and contract twice per orbit! Before Keplerian shear produces significant spreading out along the orbit it can be said that all particles will fly apart and come back together "in phase" - producing a dust cloud expands and contracts twice per orbit.

Note, however, that since the Earth's line-of-sight to the WD is for just one orbit location we will observe the dust cloud when it is at the same phase of its expansion/contraction cycle. It will therefore produce the same dip depth for every passage in front of the WD. None of our observations will reveal dust cloud changes in size between transit events.

The interesting bonus for the collision model is that every time the dust cloud contracts, the dust and any larger fragments of the source fragment will pass each other at close range with large relative velocities (on the order of 1 to 8 km/s). Ever contraction therefore affords a new opportunity for additional collisions! An initial collision may start a cascade of subsequent collisions. This could be a source for replenishing the dust cloud with new particles. 

The cascade of subsequent collisions every half orbit could replenish particles that sublimate out of existence during the time it takes for them to spread along the orbit (due to "Keplerian shear"). We don't know the timescale for particles to sublimate out of existence, but if we knew the function for particle ejection speed vs. particle size we could use the observations of dip width to model the sublimation parameters. For example, here's an observation of a dip that has a stable width of ~ 0.04 phase units (11 minutes):


Figure M09. Dip width and depth exhibiting stability for 3 months. This requires stability of dust cloud size size along orbit direction (width) and perpendicular to orbit direction (depth). Based on a waterfall plot this dust cloud was created by a collision on DOY ~ 71.

Here's the waterfall plot that exhibits dip drift lines (DLs) that diverge from an apparent creation date of DOY ~ 71.


Figure M10. Waterfall plot showing a set of drift lines (DLs) that diverge from a specific phase location at DOY ~ 71 and phase = 0.2. This DOY is presumably the date of an initial collision that created four clouds of dust and chunks of material that may have continued to collide every half orbit for the continued production of new particles and smaller chunks. Properties for DL#1 are shown in the previous figure.

Before DOY ~ 71 there was no evidence for the dust cloud under consideration, which is additional evidence that it was created by a collision on the DOY and phase associated with the DL divergence location.

Note that for the original mechanism suggested for the production of the dust clouds, sublimation jets, the dust cloud would remain the same size throughout its orbit even though the particles are constantly moving throughout the cloud (the only exception being a continual spreading out along the orbit due to Keplerian shear). For the collision model, however, particles and fragments created by a collision will be in clouds that are expanding and contracting twice per orbit, with coming together events occurring twice per orbit, for possible subsequent collisions and the creation of new particles.

Ejection Speed Requirement

What ejection speeds are required to account for the light curve observations? The deepest dips are ~ 60 %. We don't know the optical depth of the dust clouds, so consider the two extremes of totally opaque and semi-transparent. A totally opaque dust cloud that covers 60 % of the WD disk would produce the deepest dip recorded. The next figure shows how much of a disk is covered by an opaque band-shaped object with one edge intersecting disk center and the other edge located at a fraction of a radius toward a pole. For example, an opaque cloud shaped like a band (with edges aligned with the orbit) that extends from the equator to a latitude of 30 degrees will obscure 60 % of a hemisphere.


Figure M11. Blockage fraction by an opaque cloud band (parallel edges) with one edge intersecting the disk center as a function of how far the other edge extends toward a pole (blue trace). The gree trace is for an opaque band "entering" from a pole location.

Consider a dust cloud that was opaque throughout the part overlapping the WD disk (i.e., opaque to the "up/down" edges and opaque from left limb to right limb). For it to produce a dip depth of 60 % it would need a "vertical" extent of at least the WD radius. This assumes the cloud center-line passes through disk center; if the cloud band was offset from disk center such that one edge coincided with a pole the other edge would be on the other side of center at a projected latitude of 12 degrees (which makes use of the green trace in the above figure). In other words, a 60 % dip depth requires that cloud vertical extent be at least 0.6 x R_wd.

There's one problem with this opaque cloud geometry? If high opacity extended in the orbit direction beyond both limbs of the disk, by even a small amount, the dip shape would be "flat bottomed." We've never seen a "flat bottom" dip!

The optical depth
alternative is semi-transparency with a much larger cloud size. The extreme example is a cloud whose transparency is uniform across the WD disk. The deepest dip then requires that the large cloud was 40 % transparent averaged across the entire disk. We can't allow for a uniform 40 % transparency across the disk for the same reason that we are uncomfortable with the opaque cloud model: if transparency were uniform across the disk, and extended just a small amount beyond the limbs, a "flat bottom" shape would be produced. Therefore, transparency for the deepest dip (and all observed dips) must vary across the disk (i.e., along orbit direction). It would be acceptable to assume that a dust cloud is opaque at the center but the size of the opaque region must always be small in relation to the disk.

The deepest dip depth of 60 %, combined with the lack of any observed flat-bottomed dips, requires us to consider only dust cloud models that are semi-transparent averaged over solid angle regions (projected area regions) comparable to the WD disk. We are also forced to explain dust clouds with vertical extents greater than > 0.6 x R_wd. Cloud vertical extents of > 1.0 x R_wd (completely covering WD disk) is a reasonable requirement.

What ejection speeds are required for producing a cloud that completely covers the WD? Consider the case of edge-on geometry for the parent object (planetesimal, or asteroid) and the many fragments associated with that parent object and which are the source of dust clouds when they are active. The A-system of fragments has a period of ~ 4.493 hours, corresponding to a circular orbit speed of 319 km/s (assuming WD mass = 0.63 x M_earth). For particle ejection speeds that are small compared to orbital speed we can assume that up/down and in/out ejections (i..e, those with no change in orbit period) will have sinusoidal displacement variations with respect to the source orbit. For example, a 1 km/s ejection directed upward will correspond to an orbit that is inclined by 0.18 degree (57.3 x 1/319). The particle will undergo a sinusoidal displacement that takes it above the original orbit plane a distance of 2600 km (1 x 4.493 x 3600 / (2 pi)) during its first quarter orbit, then to the same distance below the orbit plane during the next half orbit, etc. Note that 2600 km is 0.31 x R_wd (assuming R_wd = 8419 km = 1.32 x R_earth). The total vertical extent of its travel will be 5200 km.

Imagine now that at the same time the first particle was ejected upward at 1 km/s another particle was ejected downward at 1 km/s. The two particles would separate across a distance of 5200 km during the first quarter orbit, come back together during the next quarter orbit, etc.. Particles ejected in the in/out directions would be in eccentric orbits with the same plane as the source orbit. These particles would have no vertical displacements. If we add a uniform distribution of directions for particles whose ejection directions are within a ring whose axis is in the orbital direction (at the time of ejection) their vertical displacements will form a (uniform) distribution of vertically displaced locations that undergo two sinusoidal expansion/contraction cycles per orbit. At the time of greatest expansion this cloud of particles will extend 5200 km, or 31 % of the WD's disk diameter.

Observers from different azimuthal directions would see the cloud as it transits the WD to have a range of sizes, from 31 % of the WD at two azimuths to just a tiny dot of ~ 0 % the size of the WD disk at azimuths differing by 90 degrees. Each observer would not know that the cloud changed size because they would always observe it at the same phase of the cloud's expansion/contraction cycle.

For those observers where a maximum size occurs at transit it is possible to calculate that a 60 % dip depth requires ejection speeds of at least 2 km/s. If the dust cloud is not opaque when it has expanded to its maximum size the required speeds exceed 2 km/s. Full disk coverage for an edge-on orientation requires speeds as high as 4 km/s. If viewing geometry is not edge-on, even greater speeds are required!

For anyone who prefers sublimation jets instead of collisions as the source of dust cloud particles the same speed requirements exist.

Radial Size

Displacements in the radial direction for the in/out particles cannot be calculated using the same concept employed for the up/down vertical displacements. Consider the case of a particle being ejected from a fragment in a circular orbit with P = 4.4930 hours traveling 319.063 km/s with an ejection speed in the forward direction of 3.19 km/s (~ 1.00 % increase of orbital velocity). The particle's radial line to the WD center of mass will sweep out an area per unit time, dA/dt, that is 1 % greater than the fragment. Circular orbits of the same central mass exhibit the relation dA/dt ~ P^1/3 (based on ratio of semi-major axis cubed being proportional to period squared). Or, P is proportional to (dA/dt)^3. So for a 1 % increase in dA/dt the new period should be 1.0303 times the original period. For the case of ejection speed = 3.19 km/s (in the forward direction) P should become 4.62914 hours, which is 0.136 hours later than the fragment after one orbit. The fragment's orbit circumference of 612.9 x R_wd, so its speed is 136.4 x R_wd / hour. The later arrival of the particle after one orbit corresponds to 18.55 R_wd, and this corresponds to a lag rate of 31 R_wd/day. Here's a summary of ejection speed and cloud size in both the vertical and radial directions for A-system dust clouds (assuming edge-on viewing geometry and opaque clouds with abrupt edges):

    Ejection         Initial          Initial          Dip      Orbit Shear
     Speed           Radius        Radius       Depth     Expansion

    0.1 km/s         250 km    0.03 R_wd      3 %     1 R_wd/day
    0.2 km/s         500 km    0.06 R_wd      7 %     2 R_wd/day
    0.5 km/s       1300 km    0.15 R_wd    20 %     5 R_wd/day
    1    km/s       2600 km    0.31 R_wd    40 %   10 R_wd/day
    2    km/s       5200 km    0.62 R_wd    72 %   20 R_wd/day
    3.2 km/s      8,400 km    1.00 R_wd  100 %   31 R_wd/day
    5    km/s    13,000 km    1.55 R_wd  100 %   49 R_wd/day

Here's an illustration, drawn to scale, of a dust cloud that can produce a 30 % dip depth, if it is opaque (as viewed from "above," looking down from a pole perspective):


Figure M12. Diagram, to scale, of the Kepler A, D and B orbits, looking "down from a pole." Symbols for dips observed during the 2015/16 season are shown at their correct orbital distances with randomly chosen orbit azimuths. The shape, labeled "Most common dip size," corresponds to a dip size that produces a dip depth of 30 % (which was common for that season). Since particles ejected with fore/aft velocity components undergo Keplerian shear they will spread out along the orbit as time progresses. The dust cloud will therefore evolve from a spherical shape to an oval shape. If the particles sublimate after a few orbits, and are replenished by collisions occurring twice per orbit after the initial collision, the oval shape can take on a steady-state shape and size. A typical steady-state length (along the orbit) is 5 x R_wd (half the width of this diagram). 

Consider the suggestion that all dust clouds pass over the WD disk center (zero impact parameter), they are semi-transparent (with no completely opague regions), and they cover the entire WD disk. Dip depth would then depend on the projected area of particles covering the disk. A dust cloud that covers the entire WD disk must have particles that were ejected at speeds as high as 3.2 km/s. In one day the 3.2 km/s particles that were ejected in the forward direction would extend behind the dust cloud center by 31 R_wd. The particles directed in the opposite direction at the same speed would be ahead of the source fragment by 31 R_wd. The total length of the cloud would be 62 R_wd, which is 520,000 km. The fragment has an orbital speed of 319 km/s, so the entire cloud would require 27 minutes to pass in front of the WD, or 0.10 phase units (that's ingress to egress, not AHS tau1 + tau2). For Dip#1 in Fig. M09, the AHS width is ~ 0.040 phase units. This corresponds to FWHM = 0.052 phase units, and 0.150 phase units for the 5 % level width. The corresponding time intervals are AHS width = 11 minutes, FWHM = 14 minutes and 5% width = 40 minutes. The ratio of 40 minutes to 27 minutes leads to a duration of 1.5 days for the fastest particles before they disappear.

The fastest particles are presumably the smallest ones produced by a collision. Is it reasonable to require that 0.5 micron radius particles disappear due to sublimation in 1.5 days? I don't know, so this will be a question for modelers to address.























Data Exchange Files   

    2015.11.21 to 2016.07.15  
    2016.10.25 to 2017.06.18  
    2017.11.10 to 2018.06.18 
    2018.11.09 to 2019.06.09 

Data exchange files are available in two formats: light curve details (one line per image) and dip fits (asymmetric hypersecant (AHS) model fits for each dip). The first of these is available for download using the above links (though 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 (AHS dip fits) may be requested from B.Gary. These may also be available here in due time.

My Collaboration Policy

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.

My observations are now "in the public domain" for this observing season (2018/19). If my data is essential to any publication just mention this in the Acknowledgement section.

 

References


    Xu, Siyi, Na'ama Hallokoun, Bruce Gary, Paul Dalba, John Debes and 14 others, 2019, "Shallow Ultraviolet Transits of WD 1145+017," arXiv 
    Gansicke, Boris + 26 others, 2019, "Evolved Planetary Systems around White Dwarfs," Astro 2020 Science White paper, arXiv
    Manser, Christopher + 31 others, 2019, "A Planetesimal Orbiting the Debris Disk around a White Dwarf Star," arXiv
    Veras, Dimitri + 8 others, 2019, "Orbital Relaxation and Excitation of Planets Tdally Interacting with White Dwarfs," arXiv  
    Vanderburg, Andrew and Saul A. Rappaport, 2018, "Transiting Disintegrating Debris around WD 1145+017," arXiv 
    Rappaport, S. B. L. Gary, A. Vanderburg, S. Xu, D. Pooley & K. Mukai, "WD 1145+017: Optical Activity During 2016-2017 and Limits on the X-Ray Flux," MNRAS, arXiv 
    Xu, S., S. Rappaport, R. van Lieshout & 35 others, "A dearth of small particles in the transiting material around the white dwarf WD 1145+017," MNRAS link, preprint arXiv: 1711.06960 
    Vanderburg et al, 2015, "A Disintegrating Minor Planet Transiting a White Dwarf," Nature, 2015 Oct 22, arXiv:1510.063387
    Croll et al, 2105, "Multiwavelength Transit Observations of the Candidate Disintegrating Planetesimal Orbiting WD 1145+017," ApJ, arXiv:1510.06434 
    Gaensicke et al, 2015, "High-Speed Photometry of the Disintegrating Planetesimal at WD 1145+017: Evidence for Rapid Dynamical Evolution," arXiv :1512.09150
    Rappaport, S., B. L. Gary, T. Kaye, A. Vanderburg, B. Croll, P. Benni & J. Foote, 2016, "Drifting Asteroid Fragments Around WD 1145+017," MNRAS, arXiv:1602.00740
    Alonso, R., S. Rappaport, H. J. Deeg and E. Palle, 2016, "Gray Transits of WD 1145+017 Over the Visible Band," Astron. & Astrophys., arXiv:1603.08823
    Petit, J.-M and M. Henon, 1986, Icarus, 66, 536-555 (link)
    Veras, Dimitri, Philip J. Carter, Zoe M. Leinhardt and Boris T. Gansicke, 2016, arXiv 
    Gary, B. L., S. Rappaport, T. G. Kaye, R. Alonso and F.-J. Hamsch, "WD 1145+017 Photometric Observations During Eight Months of High Activity," 2017, MNRAS, 465, 3267-3280. PDF  or arXiv  
    Hallakoun, N., S. Xu, D. Maoz, T.R. Marsh, V. D. Ivanov, V. S. Dhillon, M. C. P. Bours, S. G. Parsons, P. Kerry, S. Sharma, K. Su, S. Rengaswamy, P. Pravec, P. Kusnirak, H. Kucakova, J. D. Armstrong, C. Arnold, N. Gerard, L. Vanzi, 2017, Earth and Planetary Astrophysics, arXiv 1702.05486
    Farihi, J., L. Fossati, P. J. Wheatley, B. D. Metzger, J. Mauerhan, S. Bachman, B. T. Gansicke, S. Redfield, P. W. Cauley, O. Kochukhov, N. Achilleos & N. Stone, "Magnetism, X-ras, and Accretion Rates in WD 1145+017 and other Polluted White Dwarf Systems, MNRAS, arXiv
    Tom Kaye presentation at 2016 Society for Astronomical Science meeting: link   

Related Links  
    Mukremin Kilic's pro/am search of dusty WDs for dips:  https://www.nhn.ou.edu/%7Ekilic/Docs/dusty.html
    Some observing "good practices" for amateurs (book): Exoplanet Observing for Amateurs
    Hereford Arizona Observatory (HAO):  http://www.brucegary.net/HAO/
    Tutorial for faint object observing techniques using amateur hardware: http://brucegary.net/asteroids/  
    Master list of my web pages & Resume

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WebMaster:   Nothing on this web page is copyrighted. This site opened:  2018 November 29