Christian Knigge University of Southampton School of Physics & Astronoy The Secondary Stars of Cataclysmic Variables P. Marenfeld and NOAO/AURA/NSF Christian Knigge University of Southampton

Christian Knigge University of Southampton School 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?

Christian Knigge University of Southampton School of Physics & Astronoy Cataclysmic Variables: A Primer The 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 P min = 76 min –donor transitions from MS -> BD –beyond this, P orb increases again Knigge 2006

Christian Knigge University of Southampton School 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

Christian Knigge University of Southampton School 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?

Christian Knigge University of Southampton School 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 Patterson 1984

Christian Knigge University of Southampton School 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 Stehle, Ritter & Kolb 1996 Does any of this actually matter? Yes: this slight difference is key to our understanding of CV evolution!

Christian Knigge University of Southampton School 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

Christian Knigge University of Southampton School 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%! The importance of being slightly disturbed… Example 1: the period gap

Christian Knigge University of Southampton School 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 P min 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 –P min need not coincide with the donor mass reaching the H-burning limit The importance of being slightly disturbed… Example 2: the minimum period

Christian Knigge University of Southampton School of Physics & Astronoy CV donors are mostly/fully convective stars, so T eff 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-T eff one! –CV donors have the appropiate T eff (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 P orb ? –NO, because donors are still bloated compared to MS stars of the same mass! –Since, donors have lower M 2 /T eff and later SpTs than MS stars at same P The importance of being slightly disturbed… Example 3: spectral types Kolb, King & Baraffe 2001

Christian Knigge University of Southampton School 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)

Christian Knigge University of Southampton School of Physics & Astronoy Are CV donors observationally distinguishable from MS stars? Spectral Types Beuermann et al. (1998) MS StarsCV 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)

Christian Knigge University of Southampton School 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!

Christian Knigge University of Southampton School 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 M 2 = 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 M-R relation based on eclipsing and “superhumping” CVs

Christian Knigge University of Southampton School of Physics & Astronoy We have an empirical M-R relation for CV donors… … and we also expect donors to follow the MS M-T eff relation Combining these therefore yields a complete stellar parameter sequence –M 2, R 2, L 2, T eff,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

Christian Knigge University of Southampton School of Physics & Astronoy A complete, semi-empirical donor sequence (Knigge 2006) Ask me about implications for donor-based distance estimates!

Christian Knigge University of Southampton School 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?

Christian Knigge University of Southampton School 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?

Christian Knigge University of Southampton School 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 R 2 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

Christian Knigge University of Southampton School 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

Christian Knigge University of Southampton School 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

Christian Knigge University of Southampton School 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 P min (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

Christian Knigge University of Southampton School 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: M 2 = M ☼ (Littlefair et al. 2006) SDSS 1433: M 2 = M ☼ (Littlefair et al. 2008) SDSS 1501: M 2 = M ☼ (Littlefair et al. 2008) SDSS 1507: M 2 = M ☼ (Littlefair et al. 2007; Patterson et al. 2008)

Christian Knigge University of Southampton School of Physics & Astronoy Example: SDSS J1035 – the prototype! Littlefair et al. 2006

Christian Knigge University of Southampton School 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 M 2, R 2, L 2, T eff,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-T eff (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!

Christian Knigge University of Southampton School 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 P orb –However, they nevertheless follow a MS-based M 2 -T eff relation –Their M-R relation has a discontinuity at M 2 = 0.2M ☼  disrupted AML –CVs with P orb > 4-5 hrs mostly contain evolved secondaries –CVs with P orb < 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