University of Southampton

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The Secondary Stars of Cataclysmic Variables
P. Marenfeld and NOAO/AURA/NSF

• Christian Knigge
• University of Southampton

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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?

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Cataclysmic Variables A PrimerThe Orbital
Period Distribution and the Standard Model of CV
Evolution
Knigge 2006

• Clear Period Gap between 2-3 hrs
• Suggests a change in the dominant angular
  momentum loss mechanism
• Above the gap
• Magnetic Braking
• Fast AML ---gt High
• Below the gap
• Gravitational Radiation
• Slow AML ---gt Low
• Minimum period at Pmin 76 min
• donor transitions from MS -gt BD
• beyond this, Porb increases again

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Part I The Fundamental Physics of CV Secondaries

• 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 were 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

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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 a 1
• If , the donor cannot retain
  thermal equilibrium and instead responds
  adiabatically in this case (for the lowest mass
  stars) a -?
• So which is it?

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Should CV donors be on the main sequence?Time
scales above and below the gap

• With standard parameters, we find
• Thermal
• Mass-loss
• So we actually have !!!

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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

Does any of this actually matter?
Yes this slight difference is key to our
understanding of CV evolution!
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The importance of being slightly
disturbedExample 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

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The importance of being slightly
disturbedExample 1 the period gap

• 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!

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The importance of being slightly
disturbedExample 2 the minimum period

• 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 a ? !
• Note isolated brown dwarfs are never in thermal
  equilibrium and have -?

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The importance of being slightly
disturbedExample 3 spectral types

• CV donors are mostly/fully convective stars, so
  Teff is almost independent of luminosity and only
  depends on mass (Hayashi)
• So they dont 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

Kolb, King Baraffe 2001
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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
• Beuermann et al. (1998)
• Patterson et al. (2005)
• Knigge (2006)

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Are CV donors observationally distinguishable
from MS stars?Spectral Types

• Beuermann et al. (1998)

Podiadlowski, Han Rappaport (2003)
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)

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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 lt 4-5 hrs define a
  remarkably clean evolution track!

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Are CV donors observationally distinguishable
from MS stars?Masses and Radii
Patterson et al. (2005), Knigge (2006)
M-R relation based on eclipsing and
superhumping CVs

• 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)

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Putting it all together!Constructing a complete,
semi-empirical evolution track for CV donors

• 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!

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A complete, semi-empirical donor sequence(Knigge
2006)
Ask me about implications for donor-based
distance estimates!
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Are spectral types and M-R relation compatible?

• Knigge (2006)
• Yes the larger-than-MS donor radii are just
  right to account for later-than-MS SpTs!

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Part II Donors and EvolutionMagnetic 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
  donors 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?

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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 (a1, n3/2 ? Skumanich)
• Andronov, Pinsonneault Sills (2003)
• Saturated AML prescription based on open cluster
  data for CVs

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How well do we understand magnetic braking?
We dont!

• Orders of magnitude differences between recipes
  at fixed P
• Different recipes do not even agree in basic
  form!
• The saturated ones dont even beat GR below 0.5M

Knigge, Baraffe Patterson 2009
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Turning the problem aroundCan 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
  donors 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

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A First AttemptConstructing a donor-based CV
evolution track
Knigge, Baraffe Patterson 2009

• 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)

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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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Example SDSS J1035 the prototype!
Littlefair et al. 2006
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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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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 gt 4-5 hrs mostly contain evolved
  secondaries
• CVs with Porb lt 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