Cold Friends of Hot Jupiters

Identifying additional planets in transiting-planet systems, whether transiting or not, yields a wealth of information about the dynamics of the system (Fabrycky 2009). By firmly establishing the existence of additional planets in other transiting systems, it will be possible to determine if, as astronomers suspect, multipleplanet systems are common.

We propose to constrain migration mechanisms for known transiting extrasolar planets with short orbital periods by searching for stellar and/or planetary companions in long-period orbits. This search requires radial velocity monitoring with a precision of 2-3 m/s over multiple years, and we utilize the legacy of Keck HIRES data already acquired on these systems to identify systems with existing radial velocity trends as well as misaligned or eccentric orbits. These systems are prime candidates for migration processes involving interactions between either a massive stellar companion (i.e., Kozai migration) or multiple outer planets (secular migration and planet-planet scattering). Constraints on the presence or absence of additional objects in these systems therefore provide a crucial test for these migration mechanisms. These same measurements also allow us to improve current estimates for the masses and orbital eccentricities of the known short-period transiting planets in these systems.

Many of the almost 500 confirmed extrasolar planets differ significantly from their solar system counterparts. Hot Jupiters orbit at distances of less than 0.05 AU and have temperatures as high as 3000 K, comparable to cool stellar atmospheres. These planets pose a considerable challenge for planet formation models, as we know that they could not have formed at their present-day locations but instead must have migrated inward from beyond the ice line (Lin et al. 1996). By carrying out this radial velocity search for massive outer companions in systems with known short-period transiting planets, it will be possible to test competing migration models.

Hot Jupiter migration models can be broadly divided into several classes, including disk-driven migration, star-planet interactions, and planet-planet interactions. In the simplest disk migration models, including both type I and II migration, we expect the resulting short-period planets to have largely circular orbits that are well-aligned relative to the stars spin axis (e.g., Goldreich & Tremaine 1980, Tanaka et al. 2002, Lin & Papaloizou 1986). Star-planet interactions can drive inward migration in the case where the planet orbits one star in a widely separated stellar binary and where the planet’s orbit is highly inclined relative to the orbit of the second, outer star (e.g., Malmberg et al. 2007, Fabrycky & Tremaine 2007). This process is known as Kozai migration, and it causes the planet to oscillate between a highly inclined and a highly eccentric orbit; as a result we expect these systems to exhibit high orbital eccentricities and orbits that are significantly misaligned relative to the star’s spin axis. The presence of one or more additional planets in the system can produce a similar effect if the orbits of the planets are significantly inclined with respect to one another, while planetplanet scattering events can also send one planet spiraling rapidly inwards, also with a high orbital eccentricity (e.g., Chatterjee et al. 2008, Nagasawa et al. 2008). Lastly, long-term transfer of angular momentum via secular interactions in systems with three or more planets can lead to a scenario in which an initially circular planet far from its host star acquires a high orbital eccentricity and then circularizes at a new, short orbital period through tidal damping (e.g., Wu & Lithwick 2010).

The Rossiter-McLaughlin effect, where the planet produces an apparent radial velocity shift as it first occults the approaching and then the receding limbs of the rotating star, will give the spin-orbit alignment for transiting-planet systems. Significant misalignment with respect to the star's spin axis favor migration models involving either a second star or multiple planets for a significant fraction of hot Jupiters (Morton & Johnson 2011). If this is the case, we will detect the presence of additional planets or stars at wide separations in these systems using long-term radial velocity imaging. Indeed, the absence of such objects in these systems would render migration processes driven by secular instabilities unlikely.

It will also be possible to make solid inferences about the internal structures of the innermost planets. Specifically, Batygin et al. (2009b) have demonstrated that a dynamical analysis of such a system combined with models of the inner planet’s interior structure can constrain the core mass and tidal quality factor, Q, of the transiting planet. Insight into the internal structure of transiting objects can, in turn, help to constrain possible formation scenarios for the objects (Guillot 2008).

The prototypical example of such a system is the transiting planet of HATP-13. In addition to its transiting hot Jupiter, ongoing Doppler monitoring of the HAT-P-13 system (Bakos et al. 2009, Winn et al. 2010) has revealed the presence of a second and third massive perturbing planet (HAT-P-13c and HAT-P-13d) on long-period eccentric orbits. This system presents a unique opportunity to study the internal density structure as well as the efficiency of tidal dissipation in the inner transiting planet. Batygin et al. (2009b) have combined a tidal-secular orbital evolution model for HAT-P-13 with interior planetary evolution models of the inner planet, to constrain the planetary core mass to less than 120 Mearth and constrain the tidal quality factor Q to between 104 and 3105. This constraint on an exoplanetary Q factor is better than that for Jupiter. The fact that astronomers understand the interior structure of some exoplanets better than planets in our own solar system is testimony not only to the power of the proposed technique which forms the basis for this project, but also the advanced state of exoplanetary science in general. The discovery of the HAT-P-13 system has launched numerous follow-up observing campaigns that seek to refine the measurement of the planet’s radius and further constrain the core mass and Q value.

The GJ 436 system presents another set of challenges for dynamicists and theorists alike, and will likely benefit from ongoing radial velocity follow-up observations. Gliese 436b, a transiting hot Neptune with an eccentricity of 0.15, poses an unique puzzle. With no additional planets in the system, its Q factor would be larger than 107, the highest ever inferred for any planet. In the presence of additional planets, however, this object would possess a Q of order 105, similar to our ice giants (Batygin et al. 2009a). The lack of a perturber in this system may shed light on the relation between tidal Q and orbital frequency – something that has been nearly impossible to infer previously.

Professor Knutson had her proposal for observing relevant stars accepted at Keck. Her one night per semester will be added to a queue of nights award to the California Planet Search (CPS) program, led by Professor Geoff Marcy at UC Berkeley and Professor John Johnson at Caltech. A list of twenty targets was chosen, for either (1) a non-zero eccentricity, (2) a known spin-orbit misalignment, or (3) a long-term RV trend.

New coding! still working on this in idl

After finishing an RV generator for Sasha, but before making the efficiency plot, I was given another job by Professors Johnson and Knutson.

These are the directions, and the code I am working on currently.

1. get timestamps, and average precision for each target.
2. plot points, i.e.calculate the Keplerian orbit, f(t; P, e, om, Tp, msini),  where msini is directly related to K, P, e and Mstar; see this
3. plot another point some t later
4. linear fit, save the slope (use this code)
5. repeat 2) to 4) many times (in delta_v/delta_t array)
6. multiply by sqrt(Nobs)/precision to get SN_simulated
7. compare SN < SN_simulated for efficiency

Code

The larger question is whether we could find a certain sized companion planet to every system out to a given AU, maybe around 10 AU. The answer is almost certainly not, but it might have interesting implications for exoplanet research. To understand this problem a useful dispersion (maybe around RV 5, as 5 m/s is easy to get to at the 12th magnitude) and a useful sensitivity to planet mass (e.g. ~10 Jupiter masses, which is too large - maybe a tenth of that) had to be found. 

Initially, then, I found the relationship (a scaling relationship) for the mass of a planet given dispersion of its linear radial velocities (sigma), the minimum period 4*
T (taken from the baseline time from the observations) and the total number of observations N (the signal-to-noise ratio scales to the number of observations to the -1/2 power), given an assumed solar mass approximately equal to that of the sun, a circularized orbit, and a signal to noise ratio of S/N = 10. The sensitivity is below.

To better understand the theoretical considerations involved in determining the sensitivity. To do that we asked one of Caltech’s dynamicists, Konstantin Batygin. Since we are interested in learning physical things about planets, we are looking for cold friends that will give the Hot Jupiters some detectable eccentricity (which we can later on convert into a Love number). So, we are looking for eccentric outer planets. Luckily, there exists a relationship between the eccentricity ratio and the semi-major axis ratio of the pair of planets (see equation 19 of http://arxiv.org/pdf/1102.0274v1 - betas correspond to the eccentricities. 

e1/e2 ~ a1/a2

for tidally relaxed systems, or age of the system exceeding three circularization timescales given by eq.13 of http://arxiv.org/pdf/1102.0274v1. This suggests that s long as the outer companion is not much much less massive than the Hot Jupiter, the only thing that matters is the semi-major axis ratio. Consequently, larger a1/a2 is favorable for larger e1.

Bottom line:

• mass: as long as the companion is a gas giant/brown dwarf, we're good - not very sensitive to this 
• semi-major axis:1 AU is much better than 5AU. I wouldn't bother looking at 10 AU companions - e1/e2 is too small to do anything useful with.
• timescale: the Hot Jupiter itself should have had time to reach dynamical equilibrium i.e. star age >> 1 circularization timescale. 
• eccentricity: in order for the interior calculation trick to work, the outer planet must be pretty damn eccentric, so that has its own implications for the shape of the RV signal.

Our ultimate goal is to constrain the existence of x Jupiter mass planets, within y AU (maybe 2 or 5). I explored this idea with an IDL program, which inputs an RV amplitude we will be able to achieve a precision – which is dependent on the V mag of the star and the exposure time (i.e. the number of photons to reach the telescope), and the number of observations. By changing the precision, we will take a random sampling of RV measurements, and taking the population of these binned into a histogram, we can visualize the final distribution and how accurate the observations are to the actual radial velocity trend. I accomplished this in my rvmontecarlo.pro, but am trying to rewrite the code to do it backwards (more on that later).

I will try to do a monte carlo analysis, much simpler than that of in Crepp & Johnson 2011, drawing for such factors as the period of the orbit, the mass of the planet, eccentricity and others. This will have to fit with the aim of RV  4m/s and the exposure time of under 15 minutes per system. We have a total time of about 20 hrs per year, and the overhead per star is around 90 seconds/exposure, so ultimately the plan is to find stars that have interesting characteristics and that can be observed within the Keck time allotted.

It should be relatively straightforward to do this many times, assuming an observing window, and drawing randomly from an eccentricity distribution, and picking a random phase. I should try create some kind of mass-period efficiency plot for the CPS observations. This would be a really valuable exercise for the group and would constitute a real accomplishment for a SURF student.

Prioritized star list!

When I met with Sasha and Prof. Knutson in early August, we planned to do two general things.
(per Sasha)

1) coordinate with Professor Knutson to identify additional promising targets to insert into the CPS queue while the Kepler field is still available, and the number of HiRES nights is still pretty high (Aug to early fall).  These included particularly compelling targets that we may have excluded in the initial selection due to their low declination, unpublished status, etc.  August will likely be a unique opportunity to get some of these additional targets for the forseeable future. In addition, I revisited the Cold Friends proposal to look for any other particularly compelling misaligned, highly eccentric systems, or new systems indicated by Heather's personal spreadsheet.

2) get my recent study of the mass/period parameter space to a good place, working with Sasha and Tim to create a code using a Monte Carlo approach that addresses the feasibility of detecting a linear trend using the RV_Lin code and picking an observing window, eccentricity, random phase, and a given precision.  This will be an important piece of machinery to understanding the scientific limits of our program, and our ability to place constraints on these transiting systems.

The first part was accomplished well, and that's what will be discussed below. The simulation coding will be left for another post.

We were able, over the summer, to send out two shortlists of promising targets that were successfully added and observed! The following stars were sent to Professor Andrew Howard at Berkeley:

For July:  WASP-10  WASP-17  WASP-2  WASP-38  WASP-6  TrES-4
For August and September:  WASP-8  HAT-P-14  HAT-P-6  WASP-1  CoRoT-3  HAT-P-17  TrES-1 TrES-2  HAT-P-5  HAT-P-8  CoRoT-2

This was very great news. Now, to pick the stars, we followed the same justifications (eccentric, misaligned, radial velocity trend) but with the added optimization of looking at a few very specific items. First, we wanted to know the number of times CPS has observed these stars, as a lower count would be reason to increase the data set. Also, I looked at the date of the last CPS observation; if a year or more had passed, this greatly increased the priority of the star. Next, as insurance, we looked at the number of observations in the literature (pulled from exoplanets.org) which was instrumental in checking if other consortiums or projects had already well-characterized the orbit (by extra radial velocity curves) of our transiting planet. If this number was larger than the CPS observations, I assumed the star was not as important. Finally, I took the summerlst.pro procedure from earlier, and used it to find all the best observation nights of each individual star.

In conclusion, we had stars with their i) count of observations, ii) date of last observation, and iii) date of best observation, as well as iv) characteristics that made it more likely for the system to have multiple planets. It is now a matter of choosing a combination of orbital traits and the observation records, then matching it up with the best date of observation.

I set up an update 'pipeline' of sorts, with clear instructions on how to update the database with new transiting planets and new CPS observations. The instructions are below, but without the attachments. If wanted, they are easily provided.

I've included 

1) kbcvelreader.pro, which needs a) kbcvel.txt (untarred) and a file you can create called b) transitlistkeckname.txt, with the Keck names of stars you want to search kbcvel for. These files should be saved in your idl !path

2) kbcvel.ascii.tar.gzip, updated through 11 July 2011

3) transitlistkeckname.txt, with just the first 9 keck names from your list 

4) ListTwo.xlsx, which is your list of stars, with relevant information on Sheet 1. This is where RA, DEC, Vmag, Vsini, Ecc, linear trend, spin-orbit misalignment, and Obs in the literature, Keck Name, number of CPS obs, the MJD of the last CPS obs, and the last CPS obs in year/month/day formate, and the best observing night are stored.

5) summerlst.pro, which takes a file of RAs (in decimal hours) and a year, and prints out the date the star is best observed at. 

You will need

1) a file with RAs if you want to run summerlst.pro to find the day the star is best observed at

Instructions

0) updates:

   a) Update kbcvel with the new observations by CPS. I do this by unziping and untarring kbcvel.ascii.tar.gzip, exporting it to excel by i) making the headers are one string (underscores instead of spaces), then ii) delimited columns by spaces, with sequencial delimiters counting as one, and 3) shifting the first >~28000 rows of the first column left by deleting them. There might be a better way. Then I save it as kbcvel.txt.

   b) Update ListTwo with new transiting planets and their relevant information. This means:

NAME RA(hrs)   RA(deg)   DEC(deg)   Vmag Vsini Ecc λ Spin_Orbit_Mis. Obs_in_the_lit Keck_Name 

The rest of the rows will be dealt with soon 

because Keck/Andrew Howard needs RA and DEC in degrees and Vmag, and the others are interesting to the project.

1) run kbcvel.pro. This simply needs a kbcvel.txt and a transitlistkeckname.txt with all the keck names of the stars you are interested in finding 

   a) number of CPS obs 

   b) the MJD of the last CPS obs 

   c) the last CPS obs in more readable date format

Output is first an array of the stars (keckname), then an array of the count of CPS obs, then an array of the MJD, then the readable date of the last observation date. You can cut and paste these last three directly to excel columns L, M, and N.

2) run summerlst.pro:

   summerlst, 'RAfile.txt', year, /DEG

   although the year is optional, and the optional keyword /DEG is if your file has RA in decimal degrees. You can cut and paste the printed output into column O of ListTwo.xlsx.

Yep. I have my ListTwo.xlsx, which is my final product of all transiting systems, and my earlier ColdFriendsList.xlsx, with my ranked 42 top systems to investigate for cold companion planets. These are a good look at my work done.

A condensed version of my concerns and Professor Knutson's subsequent replies are below; they're really good! The kecknames, a better Vmag, and hopefully coordinate searching rather than searching by name would be an amazing idea.


Here are some answers to your questions:

1) Is WASP-13 really both htr180-001 and wasp13 for keck?

Good catch!  What led you to conclude that these are both the same star-- did you check the coordinates in the log sheets, or do you have another way of looking up observations?  It's entirely possible that WASP-13 would have a HAT candidate number-- both of these surveys observed overlapping fields, and sometimes it has been a race to see who could publish a new planet first.  Did you check to see if any other WASP planets might have been observed under htr names?

2) I think my vmag might be wrong sometimes, as they're collected from various sites. Actually about 10 different sites/papers, which included wikipedia for some kepler ones and directly from discovery papers for others (which might be outdated). So this column needs to be checked.

As Prof. Johnson mentioned, for brighter (i.e., non-Kepler) stars, SIMBAD is a good resource. You can search by star name, including names like WASP-7 or HAT-P2, or by coordinates.  In a pinch you can also probably use the Kepler magnitude or the R band magnitude instead-- just remember to flag these objects so you remember that what you used wasn't the actual V band magnitude.  For signal-to-noise calculations, any of these three magnitudes should give you equivalent answers.

3) I left vsini; as you said it's probably even better for it to have a high rotation but this way you'll have this data too!

Yes, it's useful to know vsini, both for calculating the predicted measurement precision and also for flagging systems that might be favorable targets for measuring spin-orbit alignment.

4) I really don't want to guess for keck names. There are a lot that are hrt###-### and these seem sorta random. It would be very, very nice to be able to look at a database for these and figure out for sure which keck name/names correlate with which star for certain. So I left these blank.

I know that if they have a HD or, lacking that, a HIP number these are generally it, but Kepler objects really throw me off.

Perhaps Sasha or John have some good suggestions here-- it seems like there must be a way to search the Keck data base by coordinates rather than by object name, which would ensure that we really were finding all of the observations for a given object.

The only significant data that is missing is the CPS observation count and the date (in MJD and written out) of the last observation (columns L, M, N), because of missing Keck names.

Also, I checked the wasp discovery papers (for those greater than wasp-34) and only WASP-48 kind of looked like it had a trend.

Okay, then we should probably include this star in our list of potential targets (perhaps at a bit of a lower priority, depending on how favorable of a target it turns out to be, but we can evaluate that later).

Additionally, Professor Johnson notified us that the names of all transiting stars in the Keck database are found on his computer at ~johnjohn/planets/transit.txt. I will have to figure out how to connect to the server at Cahill and retrieve this.

In conclusion, there's still a little bit of work on this section, but after rechecking these things, we'll be set for a while! Then this project can hopefully find some planets. :p

Notes

Just a few things:

Poynting–Robertson drag: solar radiation will cause dust grains to spiral inward.

From the perspective of the dust grain, solar radiation appears to be coming from a slightly forward direction. This is the aberration of light; at the instant of any observation of an object, the apparent position of the object (the sun) is displaced (see figure below). Absorbing this light leads to a force component against the direction of movement.

From the perspective of the solar system (the other reference frame), the dust absorbs sunlight in only the radial direction and its angular momentum is unchanged. However, by absorbing the photons it gains mass, and to conserve angular momentum L = r x mv, the dust must drop to a lower orbit.

Light from location 1 will appear to be coming from location 2 for a moving telescope due to the finite speed of light, a phenomenon known as the aberration of light.

Rossiter-McLaughlin effect: changes in the mean redshift of a star due to an eclipsing binary's secondary star or an extrasolar planet during transit.

A star's rotation means that at any time, one quadrant of its photosphere will be seen coming towards the viewer, and one quadrant moving away. These motions produce blueshifts and redshifts, respectively, which we observe only as spectral line broadening. However, during transit, the orbiting object blocks part of the disk, preventing some of the shifted light from reaching the observer and changing the observed mean redshift, resulting in a positive-to-negative anomaly if the orbit is prograde, and vice versa if the orbit is retrograde.

The view is situated at the bottom. The light is blueshifted on the approaching side and redshifted on the receding side. As the planet passes in front of the star it causes the star's apparent radial velocity to change.

This effect has been used to show that as many as 25% of hot Jupiters are orbiting in a retrograde direction with respect to their parents stars, strongly suggesting that dynamical interactions, rather than planetary migration, produce these objects. For cool stuff on misaligned orbits of hot Jupiters, see this.

Actually, I'll overview the link a bit. ESO claimed that "Most hot Jupiters are misaligned...the histogram of projected obliquities matches closely the theoretical distributions of using Kozai cycles and tidal friction...most hot Jupiters are formed by this very mechanism without the need to use type I or II migration." Greg Laughlin, a professor at UCSC, discusses this and comes to the conclusion that Kozai-migration, well understood for HD80606 (and explained very nicely in the post), "plays a larger role is sculpting the planet distribution than previously believed."

Electron degeneracy pressure: electrons compressed in tiny volumes gain large momentum and repulsive force

The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time, so there is a resultant repulsive force manifested as a pressure against compression of matter into smaller volumes of space. To add another electron to a given volume requires raising an electron's energy level to make room --> requirement for energy to compress the material appears as pressure.

Solid matter is...solid because of this degeneracy, instead of electrostatic repulsion. For stars which are sufficiently large, electron degeneracy pressure is not enough to prevent them from collapsing under their own weight once nuclear fusion has ceased, and then neutron degeneracy pressure prevents the star from collapsing further. In a nonrelativistic material, this is computed as:

This pressure is in addition to the normal gas pressure P = nkT / V,  and neglected unless the density (proportional to n/V) is high enough and the temperature is low enough.

The Heisenberg uncertainty principle   lets us see that as matter is condensed (uncertainty in position decreases) the momenta uncertainty increases and the electrons must be traveling at a certain speed. When the pressure due to this speed exceed that of the pressure from the thermal motions of the electrons, the electrons are degenerate.

Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.38 solar masses). This pressure prevents a white dwarf from collapsing. After the limit, the star will collapse to either a neutron star or black hole (gravity).

Paucity of intelligent life: part of this
We've highly overestimated intelligent, technologically advanced life (they would have come knocking). Why? One reason is that there is no evolutionary pressure to gain technology; another is that the lifespan of an 'advanced' civilization is perhaps on a very small order, and that they die out quickly.

Heliosphere map and IBEX: listen to this short 2009 broadcast

The sun's corona boils off into space, producing the solar wind of hot ionized gas, flowing out at a million miles an hour. This inflates the bubble of the heliosphere. IBEX, the interstellar boundary explorer, measures neutral particles that propagate in from the outer reaches of the heliosphere, about 10 billion miles out. In the space between the termination shock and the ISM, the gas becomes heated and slower. The neutralized particles are produced in this interaction region between solar-material and outer-space material. IBEX took 6 months to map these particles.

It was expected to see a variation in the particle flux, relatively small (tens of percent) and to vary over  large angular ranges. Instead, there is very narrow 'ribbon' in the sky, where the flux is two or three times of anywhere else. The ribbon appears to line up with the external magnetic field (outside of the solar field) where it drapes around and squeezes hardest on our heliosphere. Most likely, the ribbon of incoming particles is correlated to the higher density of particles outside.

Hill sphere: the region around a body where it dominates the attraction of satellites

Lies between L1 and L2, although the true region of stable satellite orbit is inside 1/2 or 1/3 of this and dependent on other forces (radiation pressure, Yarkovsky effect). Note that retrograde orbits at a wider orbit are more stable than prograde orbits. Also, in any very loworbit, a spherical body must be extremely dense in order to fit inside its own Hill sphere and be capable of supporting an orbit.

Yarkovsky effect: for small bodies (d<10km) a force caused by anisotopic thermal emmision (photons with momentum)

Roche limit: the radius at which an (only) gravitationally-bound satellite disintegrates by tidal forces.

If held together by their tensile strength (Jupiter's Metis and Saturn's Pan) satellites can orbit within their Roche limits. Almost all planetary rings are located within their Roche limit, with Saturn's E Ring and Phoebe ring being notable exceptions.

Roche lobe: the region around a star which orbiting material is gravitationally bound to the star.
If the star expands past its Roche lobe, material can escape. In a binary system escaped material will fall in through the inner Lagrangian point (mass transfer).

Vis Viva: orbital energy conservation equation; for any Kepler orbit (elliptic, parabolic, hyperbolic, or radial), the vis viva equation is , where v is the relative speed of the two bodies, r is the distance between them, and a is the semimajor axis (a>0 for ellipses, a=∞ for parabolas, and a<0 for hyperbolas).

Redshift: 

Surface Gravity: the luminosity of a star L* goes as logg*.

Kozai mechanism: the periodic exchange between inclination and eccentricity; see this.

It is a secular interaction between a wide-binary companion and a planet, in a triple system. When the relative inclination angle between the two orbital planes is greater than 39.2 degrees, known as the Kozai angle, a cyclic and long-term exchange of angular momentum occurs between the planet and more distant companion.

For an orbiting body with eccentricity e and inclination i,   is conserved. A perturbation may lead to a resonance between the two. Typcally, this results in the precession of the argument of pericenter, which then librates (oscillates) around either 90° or 270°. Increasing eccentricity while keeping the semimajor axis constant reduces the periapsis distance (the distance at closest approach), and the periapse occurs when the body is at highest inclination. The maximum eccentricity reached is independent of orbital parameters like mass and period: .

Oribital parameters, mass and semimajor axes only affect the period of the Kozai cycles. This is estimated as , where the indices are 0) central star, 1) planet, and 2) binary companion. If the Kozai period is large, it is highly unlikely the planet is highly eccentric at a given point in time. The binary companions are probably either a brown dwarf (larger orbital range, mass can approach Jupiter masses) and main-sequence dwarfs, about the mass of the sun. The Kozai period is inversely proportional to the mass of the binary companion, so oscillation periods of brown-dwarf companion systems are hundreds of times longer than that of a main-sequence dwarf star.


Just some things I should understand. :P

Exploring IDL and our stars - week ii of summer

A short update on my second week of SURF follows, as does a fuller explanation of what we are trying to do! EDIT: just the update, the theory behind is in the next post. Else this would just get long.

I was looking at the vst structure that contained the information for the radial velocity measurements that I was to look at for Professor Knutson. She got a proposal in, with a good list of stars that had certain traits (more on that in the next post), and she wanted to see whether any new measurements of these had exhibited trends since six months ago. Well, I realized that I had no idea how to work with IDL, so I got diverted into a little bit of programming to try see what I could do with it.

For my database of stars that could be interesting to observe (more on that later, e.g. next post) I wanted to know when would be the best time to observe these stars - i.e. when they were near the zenith during the year. Sasha told me that a good way of finding this would be to see which star is crossing the meridian at midnight (approximately the middle of the night) so we could say, give or take a couple days, when the star could be observed by Keck. Now, the Local Standard Time (LST) is matched exactly to the RA of a star directly overhead, which is very useful for us! All I had to do was find the LST at midnight on any particular date and match it to RA of the star to find my "perfect observing night".

Doing this by hand seemed like a little inefficient, especially if I had to find this LST and match it to more stars in the future. This lead to a little fiddling about in IDL! My program, summerlst, calls a function (LSTM()) that first populates a vector of all the LSTM for a year, without correcting for leap years. (I still kind of have to work on that part). Note that the LST @ midnight (LSTM) is 00:00 hrs at vernal equinox (Sept 21 or therabouts) and advances, as a small approximation, at 4 min a day. I introduced a tiny correction for longitude, and after 365 days, the LST cycled through 24 hrs very nicely and returned to 24:00 or 00:00 hrs. The index of this vector is a count of the number of days after Sept 21.

Then we have to match the LST with the RA of a star! There might be a better way of doing this, but I found the closest match by a difference vector (the absolute value of LST[i]-RA), then found the minimum of that, taking the index of the minimum (which will also be a count of the days after Sept 21) and figuring out which day it lands on (which includes a correction for leap year. Interesting). It outputs a nice, readable date. It would be pretty simple to instead return a Julian Date (JD) or Modified JD (MJD, where we define MJD = JD - 2.44e6 instead of what generally is put on the internet, MJD = JD - 2.4e6; that 40,000 confused me for quite a while :D) which would be more useful to the telescope but less so for knowing which star to send to the telescope, I believe.

The called function takes only a single RA, whereas the procedure is cool in that it takes an ascii file and reads it! Using more stuff from the libraries I have (the standard IDL one, the astronomy library, more :D -- cool ones I've used: ydn2md.pro and readcol.pro; cool ones I want to use: webget.pro, a function that accesses http servers and downads text and FITS files!) I define one input as an ascii file with just a list of RA that you are interested in - the RA of stars you are to observe (again, easily modified to account for a different number of columns, i.e. if the RA data is in the second column, with a star name in the first).

Now comes something I really like about IDL - that in the command line you can stop and continue programs! I printed out the no. of valid columns, i.e. the number of RA it was able to read. This should be the same as the number of stars. Then with an easy stop command, the program stops running so you can check! To continue, all you need is a .continue. SO COOL.

I used a for loop to take the RA data read in and sent it off to my LSTM function, storing the retuned string of the date (Day Month Year) in a vector that is printed out to the command line. Using for loops is slightly discouraged in IDL, as it can be slow if working with giant arrays (at least that is what I've heard). However, there are only 111 transiting planets (which is what we care about) as an upper threshhold, and currently only 42 are of any interest, and that number will be cut down given that many may not be observable this summer, it seemed the best way to go about this. If I have time later to figure out a better way of populating vectors, I will work on that.

Another really cool thing about IDL is optional keywords or inputs - which changes the direction of the program. For instance, I can input either the RA in the more common, more useful (decimal) hours, or I can take it in decimal degrees (using the /DEG keyword when running the program) and,

if keyword_set(DEG) then ra = ra / 15.

Amazing. For instance, I used the readcol procedure to read the ascii file of RA. But, since I call it with the /SILENT keyword, it doesn't print out error messages for the lines that cannot be read (i.e., empty rows or the wrong data type). Instead I just printed out the number of elements in the output vector, and ask the user if it's right (as mentioned above, with the stop command.

I ran this for the 42 stars I picked (I actually picked 40, and Prof. Knutson 20, and we only differed in two so I added those in, to make it a happy answer to life, the universe, and everything), inputed it into my database (again, more explaining next post!) and made a final spreadsheet of stars up in July! We - and when I say we, I mean the California Planet Search (CPS) - have 10 observing nights, and that should be very nice for the 8 stars we can look at!

Beginnings

It's 11:22 pm and I have been in the library for a while. Today was the first real day of SURF for me, when I actually sat down to think through the project. It was quite amazing, reading about the stars we could look at and trying to reason through which ones were more interesting - more probable to have multiple companion planets. Tomorrow I will have think about it some more. :)

But I jump ahead. Let me give a short overview of the methods we use to discover exoplanets. Currently ignoring the mostly unconfirmed Kepler Field planets, announced back in February, there are about 500 identified extrasolar planets, orbiting stars near and far (but mostly relatively close). The problem in finding exoplanets directly is obvious - the light from their sun will be generally more than a million times brighter, and it is extremely difficult to detect such a faint light source. There are some advances, by blocking starlight and interferometry, but indirect methods have proven much more effective at finding exoplanets.

Doppler spectroscopy/RV method
The most important involves radial velocity measurements. As a large planet orbits a star, it causes the parent star to wobble slightly as both objects orbit around their center of mass. The radial velocity, the speed of the star in the line of sight with Earth, changes as the star is periodically advancing towards and moving away from us. Small Doppler shifts to the light emitted by the star are detected as tiny red and blue shifts in the stars spectroscopic emission.

An exoplanet orbiting a star, both of which are orbiting their common center of mass.

When the star moves towards us, its spectrum is blueshifted, and when the star moves away from us, it is redshifted. By regularly looking at the spectrum and so measure its velocity, you can see if it moves periodically due to the influence of a companion.
Note that these shifts are tiny - literally one pixel that could be simply noise. So a very perfect template spectrum (we use HIRES' iodine cell, where HIRES is the High Resolution Echelle Spectrometer) must be overlaid against the starlight. It's quite pretty, actually, but very exacting.

The observed radial velocity can be plotted against time, and if fluctuations are periodic (circular orbits give sine waves) we have proof of a companion! Moreover, this technique, but Kepler's third law, gives a minimum mass of the planet. A nice example of 51 Pegasi's radial velocity curve is below.

51 Pegasi b, or Bellerophon, was one of earlier discovered exoplanets, and the prototypical hot Jupiter.
This is a more recent RV curve from Keck for HAT-P-6, with center of mass velocity subtracted, and residuals below it.

The largest limitation of this method is that the actual change in radial velocity is unknown, as the exoplanet is probably not on the same plane as Earth. The mass found is a minimum mass, Msini, where i is the angle of inclination.

Transit method
If a planet actually transits - passes in front of - its parent star, the star will dim by 1/10% to 1%, depending on their relative sizes. This happens pretty rarely, as the planet must be on the same plane, and there are many false positives from things like sunspots. The duration of the transit depends on the semimajor axis and the star's mass. Since the mass and size of the star can be determined from spectroscopy, the transiting planet's size and distance from the star can be calculated. If a transit even happens repeated, once per orbital revolution, it is probably a planet!

The transit affects the apparent brightness of the star.

The first exoplanet, HD 209458 b, discovered by the transit method.
One very nice thing about transits is that atmospheres can be studied, as well as parameters of the planet's surface. HD 209458 b, unofficially Osiris, is known to have an evaporating hydrogen atmosphere conaining oxygen and carbon, as well as possibly water vapor. Last year, it was announced that there was a superstorm with windspeeds of up to 7000 km/hr, by the ESO's Very Large Telescope and spectrography of carbon monoxide gas.


Now, the RV method is used to check the transit method. This summer, the plan is to take additional radial velocity measurements of exoplanets found by transits. With both the transit information and the RV curve, we might find that the systems have more than just the one exoplanet. The hope is for massive, perturbing planets on long-period eccentric orbits, pulling at the RV curve very slowly for a long term trend, which would present a unique opportunity to study the internal density structure and tidal dissipation in the inner transiting planet.

That will be for another day!

see also: Exoplanet