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Niharika SravanMidwest Relativity MeetingOctober 27, 2013Importance of Tidesfor Periastron Precession in Eccentric Neutron Star - White Dwarf Binaries

I am really honored to have been given this opportunity to share my work with such a distinguished audience. The is my first talk outside of own group at Northwestern and I am really excited to get you excited about my work. Since we have already been through three days of talks and I really want your attention, let me start off my telling you a story1Once Upon A Time

And like most stories it starts with Once upon a time, there were stars in binaries. As some of these stars orbit around each other, they would do something interesting. Their orbits would precess.2And then came the GW observer

And then came the GW observer. And there is my GW observer. His big idea was to measure GWs emiting from some of these systems in order to uncover the mysteries of the universe. You see the observer knew that GWs from such sources were emitted at multiples n of the orbital frequency. He also knew that if the system were precessing, these frequencies would be split into triplets and that the split was exactly equal to periastron precession rate over pi. You see the observer knew very well the exact physics that drove periastron precession.3Periastron PrecessionIs driven by a combination of tidal, rotational and general relativistic effects

Companion Star/Satellite

The quadrupolar periastron precession constant k2 is a measure of the WD's central concentrationHe knew it was driven by a combination of tidal, rotational and GR effects. Basically, tides are the consequence of the differential gravitational force on an extended body by a companion star/satellite. Tides produce distortions in the binary components, which perturb the stellar gravitational field from a pure keplerian form, driving precession. A similar effect arises due to rotation. So, the GW observer knows exactly how the parameters of the orbit, namely a and e, and the mass and properties of components drive precession. For systems with WD components the equations for individual components are like the following. Note simplicity of GR. Tides depend on internal structure. define k2. Complicated dependences on R_wd and k_2. So the GW observer believes that GR is the dominant driver of precession. So if a and e are known (from the frequency spectrum of the GW signal from these sources), you can infer the total system mass. So the goal here to see if this a good assumption.NOTE: k_2R5 dependence, high e, high nu.Lets start doing a test to see what the real situation can be like.

4Eccentric Neutron Star - White Dwarf binariesSeen in the field as pulsars orbiting WDsServe as probes into compact object physics that are:Clean TestableAbundant

We focus our study on eccentric NS-WD binaries. Before hitting a key: What are they?Before hitting a key: Why do we care about them?Two systems seen. See if assuming of pure GR works.5Importance of Tides and rotation in J1141-6545Is GR enough to place correct constraints on the WD mass?Currently this system has orbital frequencies bordering on SNR eLISA. So this is not a verification binary. However, it would be interesting to see the behavior of the system as its orbit tightens due to GW emission. Therefore nu increases and e decreases as a function of time So as a first check, as the system evolves through the LISA band if this system preserves an eccentricity.6

Apparently YES! Here we plot. So lets see how the various contributions to periastron precession change as the system becomes tighter and tighter7

Tides dominate in 380 MyrRotationGRTidesTotalWhat you plotThe trends in the figure demonstrate that, even though tides do not give a significant contribution to periastron precession at present, they will be the dominant mechanism after the orbit decays to frequencies > approximately 0.025 Hz in the next 380 Myr.

Since we dont have an estimate of WD age, we repeat this task for a young and hot WD entering its cooling sequence (0 Gyr old) and a 7.4 Gyr old and cold WD. Hint here: It turns out that this is true for all WD and the WD physical properties are roughly constant for most of the WD lifetime.8Galactic NS-WD binariesWe move away from the observed source and focus on pop synth predictions. Encourages pop synthesis studies for the predicted population of such systems. Pop synth predict the parameters at birth for NS-WD binaries. We would first like to see how the orbital properties change.We look at two snapshots in the lifetime of any given system, 0.5 and 13.8. The reason I pick 0.5 will be explained later. But this is early enough in the evolution of a WD.9

0.5 Gyr

13.8 GyrStarting of with parameters at birth we evolve several systems as they radiate away energy to GWs and see the parameters after 0.5 Gyr. Here we plot. Even though we start off with a near uniform distribution, we see inverse correlation. We want high e and high nu. Same for 13.8 Gyr10Our MethodHow bad can NOT accounting for tides be?we have already seen many high eccentricity and high orbital frequency systems. Test if gr is enough to account forWe start from population synthesis predictions and for a representative distribution of systems evolve orbital paramaters and WD properties simultaneously. At two ages, 0.5Gyr and 13.8Gyr we look at the current state of the system and first calculate gamma_tot11

0.5 Gyr13.8 GyrSlow and what you plot. Drive home that not accounting for tides can be bad.We also find that the effect of tides is stronger for hotter, younger WDs: 0.5 (13.8) Gyr old systems having WD masses between 0.60 and 1.03 (0.72) solar masses and eccentricities approximately less than 0.16 (0.05) suffer an error of at least 10%. So I now hear the GW observer yell out

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Alright, alright!! I get it, tides are important. But how do you expect me to accurately interpret periastron precession rate if I know nothing about the internal structure of the WD?So I now hear the GW observer yell out

And this is true. Complicated dependences. Lets look at what these dependences are,13Once again

If we simplify kr5 we could be getting somewhere. Perhaps on something already in the equations?14Facilitating mass extraction: k2RWD5 vs. MWD

Use it well.Actually, there turns out to be a relation.

0.5 Gyr came from a time when the least massive WD reaches a value of kR^5 that is held nearly constant for its lifetime. Red points.

So with this I say to the observer CLICK15ConclusionsInformation about periastron precession rates can be used to place constraints on the properties of compact object binariesTides can be a significant driver of periastron precessionThere is a simple relation that connects the WD structure parameters, governing periastron precession, to the WD mass

And with that Ill take any questions?16Questions?