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![Page 1: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/1.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
The Secondary Stars of Cataclysmic Variables
P. M
aren
feld
and
NO
AO
/AU
RA
/NS
F
Christian Knigge
University of Southampton
![Page 2: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/2.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Outline
• Introduction– The evolution of cataclysmic variables: a primer
• Part I: The Basic Physics of CV Secondaries [85%] – Theoretical overview– Observational overview
• Part II: Donors and Evolution [10%]– Magnetic braking– A donor-based CV evolution recipe
• Part III: Substellar Secondaries [ 5%]– Observed properties– Outlook
• Summary– What do we know? – What do we still need to know?
![Page 3: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/3.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Cataclysmic Variables: A PrimerThe Orbital Period Distribution and the Standard Model of CV Evolution
• Clear “Period Gap” between 2-3 hrs
• Suggests a change in the dominant angular momentum loss mechanism:
– Above the gap: • Magnetic Braking
• Fast AML ---> High
– Below the gap: • Gravitational Radiation
• Slow AML ---> Low
• Minimum period at Pmin = 76 min– donor transitions from MS -> BD
– beyond this, Porb increases again
Knigge 2006
M
M
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• The radius of a Roche-lobe filling star depends only on the binary separation and the mass ratio (Paczynski 1971)
• The orbital period depends on binary separation and masses (Kepler 1605)
• Combining these yields the well-known period-density relation for lobe-filling stars
• If we’re allowed to assume that many donors will be low-mass, near-MS stars, we expect roughly
• In that case, we have the approximate mass-period and radius-period relation
Part I:
The Fundamental Physics of CV Secondaries
3/1
3/42
13
2
q
q
a
R
)(
4
21
322
MMG
aP
2 22
132(
04
03)
1M
RG P
2 2 0.1 hrM M R R P
2 2( ) ( )R R f M M 1with f
![Page 5: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/5.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Should CV donors be on the main sequence?
Response to mass loss
• We are mainly interested in lower main-sequence stars here, where
• The response of such a star to mass loss depends on two time scales
– mass-loss time scale:
– thermal time scale:
• If , the donor remains in thermal equilibrium (and on the MS) despite the mass-loss, we have α ≈ 1
• If , the donor cannot retain thermal equilibrium and instead responds adiabatically; in this case (for the lowest mass stars) α ≈ -⅓
So which is it?
2
2
0.2 0.6 ,
0.07 0.2 ,
/
/
M radiative core large convective envelope
M no radiative core fully convective sM ta
M
r
2
2
2M
M
M
22
2 2th
GM
L R
2 thM
2 thM
![Page 6: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/6.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• With standard parameters, we find
– Thermal
– Mass-loss
• So we actually have !!!
What does that mean for the donor?
Should CV donors be on the main sequence?
Time scales above and below the gap
2 thM
1.
29
5 88 4 10
3 1010th
yrs above the gapyrs
yrs below t
M
M he gap
9 1
11 1
2
0.4
1 10
0.1
3 10
8
9
~ 4 10
~ 3 10
M yr
M
r
M
M y
M
yr above the gap
yr below the gap
Patterson 1984
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Should CV donors be on the main sequence?
Almost, but not quite…
• When , the donor cannot shrink quite fast enough to keep up with the rate at which mass is removed from the surface
• The secondary is therefore driven slightly out of the thermal equilibrium, and becomes somewhat oversized for its mass
2 thM
Stehle, Ritter & Kolb 1996
Does any of this actually matter?
Yes: this slight difference is key to our understanding of CV evolution!
![Page 8: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/8.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
The importance of being slightly disturbed…
Example 1: the period gap
• Thought to be due to a sudden reduction of AML at the upper edge (see later)
• This reduces and increases
• Donor responds by relaxing closer to its equilibrium radius
• This causes loss of contact and cessation of mass transfer on a time-scale of
• Orbit still continues to shrink (via GR), while donor continues to relax
• Ultimately, Roche-lobe catches up and mass-transfer restarts at bottom edge
• All of this only works if the donor is significantly bloated above the gap
2M2M
4 5~ ~10 ~10detach th th yR rH
![Page 9: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/9.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• How bloated must the donors be?
– Well, if there is no mass-transfer in the gap,
• From the period-density relation, we then get
• Donor at bottom edge is in or near equilibrium, so…
Donor at upper edge must be oversized by ≈30%!
2 2( ) ( )M upper edge M lower edge
2/3 2/3
2
2
( ) ( ) 31.3
( ) ( ) 2
R upper edge P upper edge
R lower edge P lower edge
The importance of being slightly disturbed…
Example 1: the period gap
![Page 10: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/10.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• Consider again the period-density relation
• Together with a simple power-law M-R relation ,
• Combining the two yields
• Differentiating this logarithmically gives
• So Pmin occurs when donor is driven so far out of equilibrium that α = ⅓ !
– Note: isolated brown dwarfs are never in thermal equilibrium and have ≈ -⅓
– Pmin need not coincide with the donor mass reaching the H-burning limit
2 32 2MP R
2 2R M
2 1 32MP
2
2
3 1
2
MP
P M
The importance of being slightly disturbed…
Example 2: the minimum period
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• CV donors are mostly/fully convective stars, so Teff is almost independent of luminosity and only depends on mass (Hayashi)
– So they don’t follow the MS M-L relation, but instead respect the M-Teff one!
– CV donors have the appropiate Teff (and SpT) for their mass
– Since they are also overluminous
• Does this mean the SpTs of CV donors should be the same as those of Roche-lobe filling MS stars at the same Porb ?
– NO, because donors are still bloated compared to MS stars of the same mass!
– Since , donors have lower M2/Teff and later SpTs than MS stars at same P
The importance of being slightly disturbed…
Example 3: spectral types
2 42 4 effL R T
2P
Kolb, King & Baraffe 2001
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
All theory is grey!
Are CV donors observationally distinguishable from MS stars?
• Until about decade ago, opinions were split
– Patterson (1984), Warner (1995), Smith & Dhillon (1998):
• CV donors are indistinguishable as a group from MS stars
– Echavarria (1983), Friend et al. (1990), Marsh & Dhillon (1995):
• CV donors have later SpTs than MS stars at the same period
• Since then, three statistical studies have attempted to clear things up
1. Beuermann et al. (1998)
2. Patterson et al. (2005)
3. Knigge (2006)
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Are CV donors observationally distinguishable from MS stars?
Spectral Types
Beuermann et al. (1998)
MS Stars CV Donors
• CV secondaries above the gap have later SpTs than MS stars at fixed P
• Above P = 4-5 hrs, SpTs show large scatter evolved secondaries?
– Yes: Podsiadlowski, Han & Rappaport (2003); Baraffe & Kolb (2000)
Podiadlowski, Han & Rappaport (2003)
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Are CV donors observationally distinguishable from MS stars?
Spectral Types
Knigge (2006)
• Double the number of SpTs (N ≈ 50 N ≈ 100)
• B98 results are confirmed
• Donors below the gap also have later SpTs than MS stars at fixed P
• Apart from a few systems with evolved secondaries, donors with P < 4-5 hrs define a remarkably clean evolution track!
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Patterson et al. (2005), Knigge (2006)
• Donors are significantly larger than MS stars both above and below the gap
• Clear discontinuity at M2 = 0.20 M☼, separating long- and short-period CVs!
– Direct evidence for disrupted angular momentum loss!
• Reasonable M-R slopes and gap / bounce masses
• Remarkably small scatter (a few percent)
Are CV donors observationally distinguishable from MS stars?
Masses and Radii
0.2gapM M
0.64
0.67
0.21
0.063bounceM M M-R relation based on eclipsing and
“superhumping” CVs
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
• We have an empirical M-R relation for CV donors…
• … and we also expect donors to follow the MS M-Teff relation
• Combining these therefore yields a complete stellar parameter sequence
– M2, R2, L2, Teff,2, log g 2
• Combining this sequence with model atmospheres additionally yields
– Absolute magnitudes
– Spectral Types
A complete, semi-empirical donor sequence specifying all physical and photometric properties along the CV evolution track!
Putting it all together!
Constructing a complete, semi-empirical evolution track for CV donors
![Page 17: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/17.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
A complete, semi-empirical donor sequence(Knigge 2006) Ask me about implications for
donor-based distance estimates!
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Knigge (2006)
• Yes: the larger-than-MS donor radii are just right to account for later-than-MS SpTs!
Are spectral types and M-R relation compatible?
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Part II: Donors and Evolution
Magnetic Braking
• All of CV evolution is driven by angular momentum losses
• Magnetic braking due to donors is critical in this respect
– Basic physics is straightforward• The donor drives a weak wind that co-rotates with donor’s B-field out to
the Alfven radius
• This spins down the donor and ultimately drains AM from the orbit
– Magnetic braking is almost certainly dominant above the gap
– It is usually assumed to stop when donor becomes fully convective, but some residual MB may also operate below the gap
• Certainly implied by observations of single stars
• May help to reconcile CV evolution theory and observations
So how well do we understand magnetic braking?
![Page 20: Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian.](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649ea95503460f94bae066/html5/thumbnails/20.jpg)
Christian Knigge University of SouthamptonSchool of Physics & Astronoy
How well do we understand magnetic braking?
A compendium of widely used recipes
• Verbunt & Zwaan (1981)– Skumanich (1972): + solid body rotation:
• Rappaport, Verbunt & Joss (1983)– VZ plus ad-hoc power-law in R2
• Kawaler (1988)– Theoretically motivated; (a=1, n=3/2 Skumanich)
• Andronov, Pinsonneault & Sills (2003)– Saturated AML prescription based on open cluster data; for CVs
• Ivanova & Taam (2003)– Another saturated recipe; for CVs
14 1/2 110eq yr sv t cm 2 22 2 2J k M R
27 2 4 32 25 10VZJ k M R
4
2RVJ VZ RJ J R
/3 21 (2 /3) 1 (4 /3),14 2 2
n nn anKaw W wK M M R RJ M
(
3;
2
;( 3/
3/2
2)
)Kaw crit
APS
Kaw n crit
n
crit
JJ
J
2( )crit M
4 3
2
4 1.3 1.7 32
j
IT
X
Xj X
K R R
K R RJ
X
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
How well do we understand magnetic braking?
• Orders of magnitude differences between recipes at fixed P
• Different recipes do not even agree in basic form!
• The saturated ones don’t even beat GR below ~0.5M☼
We don’t!
Knigge, Baraffe &Patterson 2009
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Turning the problem around:
Can we inferddddd ddfrom the donor M-R relation?
• Donors are bloated because they are losing mass
• Faster mass loss results in larger donors
• So the degree of donor bloating is a measure of a donor’s mass loss rate!
• Key advantage:
– Donor radius can provide a truly secular (long-term) mass loss rate estimate (averaged over at least a thermal time scale)
• Complications:
– Degree of bloating actually depends on mass loss history
– Tidal deformation, irradiation, activity… might also affect radii
M J and
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
A First Attempt:
Constructing a donor-based CV evolution track
Main results
• Above the gap, a standard RVJ evolution track works well!
• Below the gap, need roughly ≈2xGR!
• Comparable to recent WD-based results(Townsley & Gänsicke 2009)
• May explain larger than expected Pmin (76 min vs 65 min; e.g. Kolb & Baraffe 1999)
• May explain larger-than-expected ratio of long-to-short period CVs (Patterson1998; Pretorius, Knigge & Kolb 2006, Pretorius & Knigge 2008)
Knigge, Baraffe & Patterson 2009
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Part III: Substellar Secondaries
• Standard model:– 70% of CVs should be period bouncers with substellar secondaries
• Until very recently, only a handful of candidates but nothing definite– most famous candidate WZ Sge
• Thanks to SDSS, this situation has finally changed
– We now have at least 4 deeply eclipsing, short-period CVs with high-quality light curves and accurately measured donor masses below 0.07 M☼
• SDSS 1035: M2 = 0.052 M☼ (Littlefair et al. 2006)
• SDSS 1433: M2 = 0.060 M☼ (Littlefair et al. 2008)
• SDSS 1501: M2 = 0.053 M☼ (Littlefair et al. 2008)
• SDSS 1507: M2 = 0.057 M☼ (Littlefair et al. 2007; Patterson et al. 2008)
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Example: SDSS J1035 – the prototype!
Littlefair et al. 2006
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
So substellar donors do exist!
What else do we need to know?
• If period bouncers dominate the intrinsic CV population, it is vital that we understand their donors
– need to know M2, R2, L2, Teff,2, log g 2, SED
• We cannot rely solely on theory to guide us:
– structure and atmosphere models of BDs are still very uncertain
• No unique M-Teff (BDs cool, so age matters)• presence/absence of atmospheric dust can drastically alter the SEDs
– a substellar CV donor may differ drastically from an isolated BD
• It used to be an H-burner until recently• It is an exceptionally fast rotators (and thus perhaps abnormally active)• It is tidally deformed • It suffers strong, time-variable irradiation
We have to detect the donors directly!
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Christian Knigge University of SouthamptonSchool of Physics & Astronoy
Summary
• The last few years have seen several breakthroughs in our understanding of CV donors and their relation to CV evolution
• We now know that
– Donors are oversized relative to MS stars of equal mass
– As a result, they have later SpT than MS stars at fixed Porb
– However, they nevertheless follow a MS-based M2-Teff relation
– Their M-R relation has a discontinuity at M2 = 0.2M☼ disrupted AML
– CVs with Porb > 4-5 hrs mostly contain evolved secondaries
– CVs with Porb < 4-5 hrs follow a remarkably clean and unique evolution track
– Substellar secondaries exist!
• Key goals for the future in this area must include
– A better understanding of MB in single stars, detached binaries and CVs
– The direct detection and classification of a substellar secondary