Low-mass with Extreme Mid-Infrared Excesses: Potential Signatures of Planetary Collisions

Dissertation Defense Talk

Christopher A. Theissen July 17, 2017 Driving Questions

• How often do low-mass stars in the field exhibit extreme MIR excesses?

• What are the physical trends we observe for low- mass stars exhibiting extreme MIR excesses?

• Do binary systems exhibit extreme MIR excesses more often than single stars? /planet formation in a nutshell

Spectral Energy Distribution

Peaks in the far-IR < 10,000 years

Peak flux moves to shorter wavelengths ~100,000

Star is now visible in the optical ~ 1 million years

Flux dominated by star, with a potential small >10 million years MIR excess André (1994) “Extreme” MIR Excesses

Weinberger+ (2011) “Extreme” MIR Excesses

1 billion old binary system!

Weinberger+ (2011) What is the interpretation?

Credit: NASA/JPL Collisions between terrestrial planets What is the interpretation?

Credit: NASA/JPL

Credit: S. Raymond Seven systems currently known

HD 23514 HD 15407 ID8

360 AU 1200 AU

120 Myr 80 Myr 35 Myr

P1121 TYC-8241-2652-1 BD +20 307 TYC-8830-410-1

0.04 AU

80 Myr 10 Myr 1 Gyr ? Seven systems currently known

HD 23514 HD 15407 ID8

360 AU 1200 AU All solar-type (FGK) stars. 120 Myr 80 Myr 35 Myr Why are there no low-mass stars in the sample? P1121 TYC-8241-2652-1 BD +20 307 TYC-8830-410-1

0.04 AU

80 Myr 10 Myr 1 Gyr ? What exactly is a “low-mass” star? • Less than 60% the mass of the Sun

• Cool stars (Temperatures < 4600 K)

• Red dwarfs

• M dwarfs

Credit: NASA They have incredibly long () lifetimes

Current Age of the Universe 10

1

0.1

Lifetime (billion yrs) 0.01

0.9M ⇠ 0.001 0 10 20 30 40 Mass (M ) They have incredibly long (main sequence) lifetimes

Low-mass stars live here Current Age of the Universe 10

1

0.1

Lifetime (billion yrs) 0.01

0.9M ⇠ 0.001 0 10 20 30 40 Mass (M ) Low-mass Stars are Everywhere

Todd J. Henry1 Ten Census 2010 Mark R. Boyd2 Serge Dieterich1 www.recons.org Charlie T. Finch3 Wei-Chun Jao1 Adric R. Riedel1 John P. Subasavage4 Jennifer G. Winters1

1GSU, 2GaTech, 3USNO, 4CTIO

~70% of all stars are low-mass stars

2010 20 4 6 20 44 246 4 9 13+8 WD A F G K M L T P 2000 18 4 6 20 44 198 0 1 2+8

Credit: RECONS Low-mass Stars are Everywhere (with Earth-sized Planets!)

Todd J. Henry1 Ten Parsec Census 2010 Mark R. Boyd2 Serge Dieterich1 www.recons.org Charlie T. Finch3 Wei-Chun Jao1 Adric R. Riedel1 John P. Subasavage4 Jennifer G. Winters1

1GSU, 2GaTech, 3USNO, 4CTIO

• ~70% of all stars are low-mass stars

2010 20 4 6 20 44 246 4 9 13+8 WD A F G K M L T P 2000 18 4 6 20 44 198 0 1 2+8

Credit: RECONS Planets orbit close-in

Credit: Muirhead+ (2012)/NASA Planets orbit close-in

Credit: Gillon+ (2016, 2017)/NASA The Kepler Dichotomy

Kepler has found lots of multi- and single-transiting planetary systems. • Both populations cannot be explained by the same planetary architecture (Ballard & Johnson 2016).

Multi-planet model excluding Multi-planet model Multi-planet model single-transiting systems with eccentricities

Ballard & Johnson (2016) The Kepler Dichotomy Mixture model for a dual population

Singles Multis

slower stellar faster stellar rotation rates rotation rates

farther from the closer to the Galactic plane Galactic plane

Ballard & Johnson (2016) The Kepler Dichotomy Mixture model for a dual population

Singles Multis Older? Younger? slower stellar faster stellar rotation rates rotation rates

farther from the closer to the Galactic plane Galactic plane

Ballard & Johnson (2016) Driving Questions

• How often do low-mass stars in the field exhibit extreme MIR excesses?

• What are the physical trends we observe for low- mass stars exhibiting extreme MIR excesses?

• Do binary systems exhibit extreme MIR excesses more often than single stars? Using M Dwarfs

The spectroscopic sample The photometric sample M0 M4 M6 M8 L0 105 WISE+SDSS+2MASS SDSS+2MASS 104 WISE+SDSS SDSS+USNO-B 103

102 # of Stars

101

Mass Increasing 100

100 Theissen+ (2016) West+ (2011)

1 10

2 10

3 10 Normazlied Distributions

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 r z Building the photometric sample Motion Verified Red Stars (MoVeRS)

3.5 5 5

3.0 SDSS + SDSS + SDSS 4 4 2.5 2MASS WISE

3 3 2.0 i z z − − − r 1.5 r r 2 2

1.0 1 1 0.5

0.0 0 0 0.00.51.01.52.0 0.51.01.52.02.53.0 1.01.52.02.53.03.54.04.55.0 i − z z − J z − W 1 Theissen+ (2016)

1 arcminute Building the photometric sample Motion Verified Red Stars (MoVeRS)

3.5 5 5

3.0 SDSS + SDSS + SDSS 4 4 2.5 2MASS WISE

3 3 2.0 i z z − − − r 1.5 r r 2 2

1.0 1 1 0.5

0.0 0 0 0.00.51.01.52.0 0.51.01.52.02.53.0 1.01.52.02.53.03.54.04.55.0 i − z z − J z − W 1 Theissen+ (2016)

1 arcminute …and the Late-Type Extension to MoVeRS (LaTE-MoVeRS)

600 9 3750 3500 500 10 3250 11 400 3000 J 12 2750 (K) 300 M 2500 e ↵ 13 T # of Stars 200 2250 14 2000 100 Field sequence 15 Young sequence 1750

0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 350 400 450 J K Theissen+ (2017) d (pc) Theissen+ (2017)

~47,000 late-type objects with temperatures < 3800 K …and the Late-Type Extension to MoVeRS (LaTE-MoVeRS)

600 9 3750 3500 500 10 3250 11 400 3000 J 12 2750 (K) 300 M 2500 e ↵ 13 T # of Stars Complimentary to Gaia 200 2250 14 2000 100 Field sequence 15 Young sequence 1750

0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 350 400 450 J K Theissen+ (2017) d (pc) Theissen+ (2017)

~47,000 late-type objects with temperatures < 3800 K Selecting M Dwarfs with Excess MIR Flux

The spectroscopic sample The photometric sample 500 400 8 5 300 Full Sample 103 200 Excess significance 4

#stars 100 0 3 6 −10 01020304050 3 W σ′ 2 3 1

W 2 4 10

Stars with W − 1 1 excess W MIR flux 0 2

Clean Sample 101 Stars 2 # of Stars 0 3 234567891011 W MW 1 1

Theissen & West (2014) 1 100 W

0

Multiple criteria to select 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 r z Theissen & West (2017) stars with excess MIR flux. Spectral Energy Distributions for Extreme MIR Excesses The spectroscopic sample The photometric sample −10 9 152 SpT = dM1 SDSS +100 objID = 1237678920195637464 T +79 )] ∗ =3600 K −100 )] T = 3105 K 2MASS 2 21 +10 2 ⇤ − WISE TIR =175 K Tdust = 209 47K −10 10 ± cm −11 cm 1 1 − 11 (erg s (erg s λ −12 F F λ 12 Log [ Log [

13 −13 110 1 10 λ (µm) (µm) Theissen & West (2014) Theissen & West (2017) Aging M Dwarfs: Hydrogen Emission aka “Activity”

West+ (2008) Hydrogen Emission

Obtained DCT (and dM7 SDSS) optical spectra

dM6 of randomly selected

o ↵ set stars.

+ dM5

dM4 Scaled Flux dM3

dM2

dM0

6000 6500 7000 7500 8000 8500 Wavelength (A)˚

Adapted from Theissen & West (2017) Hydrogen Emission

Obtained DCT (and dM7 SDSS) optical spectra

dM6 of randomly selected

o ↵ set stars.

+ dM5

dM4 Stars later than M4 are inactive, indicating a Scaled Flux dM3 field population likely

dM2 Inactive Stars older than a few billion years dM0

6000 6500 7000 7500 8000 8500 Wavelength (A)˚

Adapted from Theissen & West (2017) Know Thy Star, Know Thy Disk

5000 6th Order Polynomial 105 Dartmouth ([Fe/H] = 0) 5 Gyr 4500 Dartmouth ([Fe/H] = 0) 10 Gyr 104 4000 Dartmouth ([Fe/H] = -2.4) 10 Gyr Mann et al. 2015 103 (K) 3500

e ↵ 2 T 3000 10 # of Stars 2500 101 2000 100 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Theissen & West (2017) r z 1.0 105 0.8 104

0.6 Temperatures estimates from 103 /R ⇤

SED fits. R 0.4 102 # of Stars

1 Radius estimates from SED 0.2 10

100 fits + distances. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 r z Know Thy Star, Know Thy Disk

The spectroscopic sample The photometric sample

Theissen & West (2017) Theissen & West (2014) Driving Questions

• How often do low-mass stars in the field exhibit extreme MIR excesses?

• What are the physical trends we observe for low- mass stars exhibiting extreme MIR excesses?

• Do binary systems exhibit extreme MIR excesses more often than single stars? Model of the (Nearby) Galaxy

35 102 RECONS RECONS Survey 30 LoKi LoKi Limit

25 101 20

15 # of Stars # of Stars 10 100 5

0 0 0 5 10 15 20 25 101 102 103 104 Distance (pc) Total (mas/yr) Theissen & West (2017)

Model of low-mass stars and their kinematics in our Galaxy

The Low-mass Kinematics model (LoKi) Model of the (Nearby) Galaxy

35 102 RECONS RECONS Survey 30 LoKi LoKi Limit

25 101 20

15 # of Stars # of Stars 10 100 5 Available on GitHub! 0 0 0 5 10 15 20 25 101 102 103 104 Distance (pc) Total Proper Motion (mas/yr) Theissen & West (2017)

Model of low-mass stars and their kinematics in our Galaxy

The Low-mass Kinematics model (LoKi) What percentage of low-mass field stars exhibit extreme MIR excesses?

~0.04% of low-mass stars exhibit extreme MIR excesses What percentage of low-mass field stars exhibit extreme MIR excesses?

~0.04% of low-mass stars exhibit extreme MIR excesses

as compared to 0.0007% of solar- type stars (AFGK-spectral types) Driving Questions

• How often do low-mass stars in the field exhibit extreme MIR excesses?

• What are the physical trends we observe for low- mass stars exhibiting extreme MIR excesses?

• Do binary systems exhibit extreme MIR excesses more often than single stars? Is there a mass trend? M0 M4 M6 M8 L0 0.00200 Lower mass 0.00175

0.00150

0.00125

0.00100

0.00075

0.00050

0.00025 Extreme MIR Excess Fraction 0.00000 1 2 3 4 5 r z Theissen & West (2017) There might be a slight trend with , indicating lower- mass stars are more likely to host an extreme MIR excess Is there an age trend?

Credit: M. Ness/MPIA Stars further away from the Galactic plane are, on average, older Is there an age trend?

Older

Older

Credit: M. Ness/MPIA Stars further away from the Galactic plane are, on average, older Is there an age trend?

The spectroscopic sample The photometric sample Older 0.0008

0.0006

0.0004

0.0002 Older Extreme MIR Excess Fraction 0.0000 200 400 600 Z (pc) | | Theissen & West (2014) Theissen & West (2017)

# stars w/ MIR excess Fraction = Total # stars Is there an age trend?

The spectroscopic sample The photometric sample Older 0.0008

0.0006

Incomplete 0.0004

0.0002 Older Extreme MIR Excess Fraction 0.0000 200 400 600 Z (pc) | | Theissen & West (2014) Theissen & West (2017)

# stars w/ MIR excess Fraction = Total # stars Driving Questions

• How often do low-mass stars in the field exhibit extreme MIR excesses?

• What are the physical trends we observe for low- mass stars exhibiting extreme MIR excesses?

• Do binary systems exhibit extreme MIR excesses more often than single stars? Seven systems currently known

HD 23514 HD 15407 ID8

360 AU 1200 AU

120 Myr 80 Myr 35 Myr

P1121 TYC-8241-2652-1 BD +20 307 TYC-8830-410-1

0.04 AU

80 Myr 10 Myr 1 Gyr ? White Dwarf + M Dwarf Binaries (WD+dM)

Similar binaries, but with different peaks in their spectral energy distributions.

Can be detected with low- to moderate-resolution spectra. Morgan+ (2012) Two Binaries Found

10 SDSS Spectrum SDSS Spectrum BT-Settl (2806 K) BT-Settl (3017 K) 10 TWD (8378 K) TWD (7131 K) SDSS SDSS 2MASS 2MASS

)] 11 WISE )] WISE 2 2

unWISE unWISE 11 cm cm 1 1

12 (erg s (erg s

12

F F

Log [ 13 Log [ 13

14 1 10 1 10 (µm) Theissen+ in prep. (µm) Two Binaries Found Plus One

10 SDSS Spectrum SDSS Spectrum BT-Settl (2806 K) BT-Settl (3017 K) 10 TWD (8378 K) TWD (7131 K) SDSS SDSS 2MASS 2MASS

)] 11 WISE )] WISE 2 2

unWISE unWISE 11 cm cm 1 1

12 (erg s (erg s

12

F F

Log [ 13 Log [ 13

14 1 10 1 10 (µm) Theissen+ in prep. (µm)

Debes+ (2012) What percentage of WD+dM systems exhibit extreme MIR excesses?

~0.04% of WD+dM systems exhibit extreme MIR excesses What percentage of WD+dM systems exhibit extreme MIR excesses?

~0.04% of WD+dM systems exhibit extreme MIR excesses

These are small number statistics with no way to account for completeness yet. More work is needed. Conclusions

• How often do low-mass stars in the field exhibit extreme excess MIR flux?

• Approximately 0.04% of low-mass field stars exhibit extreme MIR excesses (versus 0.0007% for solar-type stars).

• What are the trends we observe for low-mass stars exhibiting extreme MIR excesses?

• An age trend is observed, with younger field stars exhibiting a higher incidence of extreme MIR excesses over older field populations

• There may be a mass dependence, with lower-mass stars more likely to exhibit an extreme MIR excess.

• Do binary systems exhibit extreme MIR excess more often than single stars?

• Using WD+dM systems, I find binaries typically host dust as often as single stars. Origins may be vastly different though. Acknowledgements (No one does it alone) Aging SDSS M Dwarfs I: Surface Gravity

Dwarf

Body Level One Body Level Two Body Level Three Body Level Four Normalized Flux Normalized Body Level Five Giant

Mann+ (2012)

Theissen & West (2014) Aging SDSS M Dwarfs II: Hydrogen emission

Morgan et al. (2012) Aging SDSS M Dwarfs II: Hydrogen emission

Theissen & West (2014) Building the Photometric Sample Motion Verified Red Stars (MoVeRS)

M0 M4 M6 M8 L0 105 SDSS+USNO-B WISE+SDSS+2MASS SDSS+2MASS WISE+SDSS WISE+SDSS+2MASS 10 SDSS+2MASS 104 104 WISE+SDSS SDSS+USNO-B 103

102 15 103 # of Stars

101

100 r

0 H 10 20 102 #ofStars

1 10

1 2 25 10 10

3 10 Normazlied Distributions

−1 vT =180kms 30 100 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 12345 12345 12345 12345 r z r − z r − z r − z r − z Theissen+ (2016) Theissen+ (2016) Using MoVeRS: Defining the Sample

400 pc 100 pc 20 pc Sensitive to 12 Stars & Disks 17 )] Sensitive to Disks 2

18 cm 1 r 19 13 3 Stellar Flux W 20 [(ergs s AV =0.2 10 21 log

14 Expected 1 2 3 4 5

r z Theissen & West (2017) Contamination Rate? Giants verus Dwarfs ˚ A)

0 Candidate stars tend to follow

Ti I (6497 10 , the dwarf population.

Mn I 20

, DCT

Fe I 30 Peculiar ~4% contamination , SDSS

Ba II 2.00 Giants (68%) 60 Giants (99%) 1.75 Dwarfs (68%) Dwarfs (99%) ˚ A) 1.50 40

1.25

20 Na I (5893 CaH2 + CaH3 1.00

0.75

4 4 ˚ A) ˚ A) 2 2 K I (7665

0 Na I (8189 0

2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 TiO5 TiO5 Theissen & West (2017) 5000 6th Order Polynomial 105 Dartmouth ([Fe/H] = 0) 5 Gyr 4500 Dartmouth ([Fe/H] = 0) 10 Gyr 104 4000 Dartmouth ([Fe/H] = -2.4) 10 Gyr Mann et al. 2015 103 (K) 3500

e ↵ 2 T 3000 10 # of Stars 2500 101 2000 100 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 r z 1.0 1.0 105 105 This study 0.8 Mann et. al. 2015 0.8 104 104 Boyajian et al. 2012

0.6 3

0.6 103 10 /R /R ⇤ ⇤ 2 R R 0.4 102 0.4 10 # of Stars # of Stars

1 0.2 10 0.2 101

0 10 0.0 100 0.0 2000 2500 3000 3500 4000 4500 5000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 T (K) r z e↵ Theissen & West (2017) Youth Tracers Part Deux

dM7

dM6 dM7

dM5 dM7 Obtained SDSS and dM5 DCT optical spectra dM6 dM5 of randomly dM4

dM5 dM4 selected stars.

dM4 dM4

dM3 Scaled Flux + o ↵ set dM3 Scaled Flux + o ↵ set dM3 Stars are again dM2 dM3 consistent with the

dM2 dM2 field population.

dM2

dM1 dM2

dM0 dM1

4000 5000 6000 7000 8000 9000 6000 6500 7000 7500 8000 8500 (A)˚ (A)˚ Theissen & West (2017) Model of the (Nearby) Galaxy

35 50 RECONS SUPERBLINK 30 LoKi LoKi 40 Model of the low- 25 mass stars and their 20 30

15 kinematics in our 20 # of Stars # of Stars 10 Galaxy 10 5

0 0 0 5 10 15 20 25 0 10 20 30 40 50 60 The Low-mass Distance (pc) Distance (pc) Kinematics model 102 102 RECONS Survey SUPERBLINK LoKi Survey Limit LoKi Limit (LoKi)

101 101 # of Stars # of Stars

100 100

0 0 101 102 103 104 101 102 103 104 Total Proper Motion (mas/yr) Total Proper Motion (mas/yr) Theissen & West (2017) Model of the (Nearby) Galaxy

35 50 RECONS SUPERBLINK 30 LoKi LoKi 40 Model of the low- 25 mass stars and their 20 30

15 kinematics in our 20 # of Stars # of Stars 10 Galaxy 10 5

0 0 0 5 10 15 20 25 0 10 20 30 40 50 60 The Low-mass AvailableDistance (pc) onDistance (pc) GitHub!Kinematics model 102 102 RECONS Survey SUPERBLINK LoKi Survey Limit LoKi Limit (LoKi)

101 101 # of Stars # of Stars

100 100

0 0 101 102 103 104 101 102 103 104 Total Proper Motion (mas/yr) Total Proper Motion (mas/yr) Theissen & West (2017) Is There an Age Effect?

Galactic Stratigraphy

Adapted from West et al. (2011) What are the trends with MIR excesses?

M0 M4 M6 M8 L0 0.00200

0.0008 0.00175 Lower mass

0.00150 0.0006 0.00125

0.00100 0.0004 0.00075

0.0002 0.00050 0.00025 Extreme MIR Excess Fraction Older Extreme MIR Excess Fraction 0.0000 0.00000 200 400 600 1 2 3 4 5 Z (pc) Theissen & West (2017) r z | |

Younger field stars are more likely to host an extreme MIR excess

There might be a slight trend with stellar mass, indicating lower-mass stars are more likely to host an extreme MIR excess What are the trends with MIR excesses?

0.5 r z<2.0 2.0 r z<3.5 3.5 r z<5.0 0.0005  0.0020  0.0025 

0.0004 0.0020 0.0015

0.0003 0.0015 0.0010 0.0002 0.0010

0.0005 0.0001 0.0005

Extreme MIR Excess0 Fraction .0000 0.0000 0.0000 0 200 400 600 800 0 100 200 300 0 50 100 Z (pc) Z (pc) Z (pc) | | | | | | Theissen & West (2017) Locating Binaries

Very tight binaries require high-resolution spectroscopy (over multiple epochs) to find.

Weinberger (2008) Locating Binaries

Intermediate separation binaries require high- resolution adaptive optics imaging

Bardalez-Gagliuffi+ (2015) Current Samples with MIR Excesses

60 WD+dM

50 Using available samples, selected 40 WD+dM systems µ =0.33 30 =0.19 with excess MIR flux

# of20 Systems WD+dMs with 10 MIR Excesses

0 0 2 4 6 W 1 W 3 Theissen+ in prep. A Tool for Measuring WISE Source Quality

950 960 970 980 990 950 960 970 980 990

100000 W1 100000 W2 0 0 1225 N 1225 1225 N 1225 A tool to measure E E 1220 1220 1220 1220 1215 1215 1215 1215 source “roundness” 1210 1210 1210 1210

1205 1205 1205 1205 and band-to-band

1200 1200 1200 1200 Decl. (pixel) Decl. (pixel) correlation. 1195 1195 1195 1195

1190 1190 1190 1190

1185 1185 1185 1185 950 960 970 980 9900 100000 950 960 970 980 9900 100000 R.A. (pixel) R.A. (pixel) The unWISE Intrinsic 950 960 970 980 990 950 960 970 980 990 Source Estimator for 100000 50000 W3 W4 0 0 Sureness and 1225 N 1225 1225 N 1225 E E 1220 1220 1220 1220 Trustworthiness 1215 1215 1215 1215 (unWISEST) 1210 1210 1210 1210

1205 1205 1205 1205

1200 1200 1200 1200 Decl. (pixel) Decl. (pixel)

1195 1195 1195 1195

1190 1190 1190 1190

1185 1185 1185 1185 950 960 970 980 9900 100000 950 960 970 980 9900 50000 R.A. (pixel) R.A. (pixel) Theissen+ in prep. A Tool for Measuring WISE Source Quality

950 960 970 980 990 950 960 970 980 990

100000 W1 100000 W2 0 0 1225 N 1225 1225 N 1225 A tool to measure E E 1220 1220 1220 1220 1215 1215 1215 1215 source “roundness” 1210 1210 1210 1210

1205 1205 1205 1205 and band-to-band

1200 1200 1200 1200 Decl. (pixel) Decl. (pixel) correlation. 1195 1195 1195 1195

1190 1190 1190 1190

1185 1185 1185 1185 950 960 970 980 9900 100000 950 960 970 980 9900 100000 The unWISE Intrinsic R.A.Available (pixel) R.A. (pixel)on GitHub! 950 960 970 980 990 950 960 970 980 990 Source Estimator for 100000 50000 W3 W4 0 0 Sureness and 1225 N 1225 1225 N 1225 E E 1220 1220 1220 1220 Trustworthiness 1215 1215 1215 1215 (unWISEST) 1210 1210 1210 1210

1205 1205 1205 1205

1200 1200 1200 1200 Decl. (pixel) Decl. (pixel)

1195 1195 1195 1195

1190 1190 1190 1190

1185 1185 1185 1185 950 960 970 980 9900 100000 950 960 970 980 9900 50000 R.A. (pixel) R.A. (pixel) Theissen+ in prep. Circumbinary Dust

Farihi+ (2017)

Dust orbits both components of the binary WD+dMs with Dust These are all interacting binaries

Hoard (2013)