The Secondary Stars of Cataclysmic Variables

1. The Secondary Stars of Cataclysmic Variables Christian Knigge University of Southampton P. Marenfeld and NOAO/AURA/NSF

2. 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?

3. 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

4. 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 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

5. 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?

6. Patterson 1984 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 !!! What does that mean for the donor?

7. Stehle, Ritter & Kolb 1996 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!

8. 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

9. The importance of being slightly disturbed…Example 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%!

10. The importance of being slightly disturbed…Example 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 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

11. The importance of being slightly disturbed…Example 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 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 Kolb, King & Baraffe 2001

12. 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)

13. Are CV donors observationally distinguishable from MS stars?Spectral Types Podiadlowski, Han & Rappaport (2003) 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)

14. 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!

15. Are CV donors observationally distinguishable from MS stars?Masses and Radii 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) M-R relation based on eclipsing and “superhumping” CVs

16. 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, logg2 • 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!

17. A complete, semi-empirical donor sequence(Knigge 2006) Ask me about implications for donor-based distance estimates!

18. 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!

19. 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 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?

20. 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

21. How well do we understand magnetic braking? We don’t! • 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☼ Knigge, Baraffe & Patterson 2009

22. 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

23. A First Attempt:Constructing 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)

24. 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)

25. Example: SDSS J1035 – the prototype! Littlefair et al. 2006

26. 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, logg2, 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!

27. 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