christian knigge university of southampton school of physics & astronoy the secondary stars of...

Christian Knigge University of SouthamptonSchool of Physics & Astronoy

The Secondary Stars of Cataclysmic Variables

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Christian Knigge

University of Southampton


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?


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


• 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

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RG P

2 2 0.1 hrM M R R P

2 2( ) ( )R R f M M 1with f


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 ,

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M radiative core large convective envelope

M no radiative core fully convective sM ta

M

r

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22

2 2th

GM

L R

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2 thM


• With standard parameters, we find

– Thermal

– Mass-loss

• So we actually have !!!

What does that mean for the donor?


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

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1 10

0.1

3 10

8

9

~ 4 10

~ 3 10

M yr

M

r

M

M y

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yr above the gap

yr below the gap

Patterson 1984



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!


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


• 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


Example 1: the period gap


• 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


Example 2: the minimum period


• 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


Example 3: spectral types

2 42 4 effL R T

2P

Kolb, King & Baraffe 2001


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)



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)



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!


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)


Masses and Radii

0.2gapM M

0.64

0.67

0.21

0.063bounceM M M-R relation based on eclipsing and

“superhumping” CVs


• 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


A complete, semi-empirical donor sequence(Knigge 2006) Ask me about implications for

donor-based distance estimates!


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?


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?


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

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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


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


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


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 1507: M2 = 0.057 M☼ (Littlefair et al. 2007; Patterson et al. 2008)


Example: SDSS J1035 – the prototype!

Littlefair et al. 2006


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!


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

christian knigge university of southampton school of physics & astronoy the secondary stars of...

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