# RV- method: disturbing oscilla8ons Example: F- star Procyon

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1 Star spots

2 RV- method: disturbing oscilla8ons Example: F- star Procyon

3 In- class ac8vity (1) 1) You are working with the HARPS instrument and you want to unambiguously detect Jupiter-twins around nearby G stars. Because you are famous you can have as many observing nights as you want, but you have to tell the observatory for how many years you would like to access the telescope. Given the unprecedented precision of HARPS A) ~1 year of telescope access is needed for your science goal B) ~6 years of telescope access are needed for your science goal C) ~12 years of telescope access are needed for your science goal 2) As already mentioned in the lecture, all exoplanet detection techniques include certain biases. From what you have heard and read, compile a list and discuss potential biases of the RV method.

4 A planet around the nearest star found by RV Nature, August 2016

5 - - - Planet rates from RV- surveys dots are planet detec8ons (red considered, black not considered in sta8s8cs) lines are detec8on probabili8es dashed lines give parameter range for derived planet rates M2sini [Earth Mass] planetary rate: 14% ± 2 100% 95% 80% 60% 40% 20% 10% 5% 2% M2sini [Earth Mass] % ± 7 95% 80% 60% 40% 20% 10% 5% 2% Period [days] Fig. 6. Same as Fig. 5 with detection probability curves superimposed. These detection probabilities are valid for the whole sample giant of 822 planets stars. AfterP correcting < 10 for yr the detection bias, the fraction of stars with at least one planet more massive than 50 M and with a period smaller than 10 years is estimated to be 14 ± 2 %. The red points represent the planets which have been Period [days] Fig. 7. Same as Fig. 5 but only for the HARPS subsample. The occurrence rate of planetary systems in the limited region between 3 and 100 M, and with P < 1 year, is 47 ± 7 %. Again, only the red dots and the blue triangles (candidates) have been considered for the computation of the occurrence rate. planets between 3 and 100 M earth and P<1 year Mayor et al (

6 - - - Planet rates from RV- surveys dots are planet detec8ons (red considered, black not considered in sta8s8cs) lines are detec8on probabili8es dashed lines give parameter range for derived planet rates ± M2sini [Earth Mass] % ± % ± % ± % ± 2 17% ± 4 24% ± Period [days] 100% 95% 80% 60% 40% 20% 10% Fig. 9. Same as Fig. 6. The dashed lines represent the boxes in which the occurrence rate is computed as defined by Howard et al. (2010). An additional box is shown for masses between 1 and 3 M. (Bonfils & al. 2011). Despite the rather limited range of stellar masses in our sample, we have tried a comparison of the (m 2 sin i log P) distribution for dwarf stars of spectral type F and G versus the distribution for K dwarfs. The observed di er- 5% 2% 4.3. The mass distribution On Fig.10 we have plotted the histogram of masses of the planets detected in our sample. We observe a drastic decline of the observed mass distribution from about 15 to 30 M. If we limit the range of orbital periods and only consider planets with P < 100 days (Fig. 11), a region where the detection bias are not too important for low-mass planets, we immediately observe the preponderant importance of the sub-population of super-earths and Neptune-mass planets in that domain of periods. After correction of detection biases (Fig. 12), we see even more clearly the importance of the population of low-mass planets on tight orbits, with a sharp decrease of the distribution between a few Earth masses and 40 M. We note that the planet population synthesis models by Mordasini et al. (2009b) predicted such a minimum in the mass-distribution at precisely this mass range. They also pointed out that a radial-velocity measurement precision of about 1 ms 1 was required in order to detect this minimum. In the framework of the core accretion model, this can be understood by the fact that this mass range corresponds to the runaway gas accretion phase during which planets acquire mass on very short timescales. Therefore, unless timing is such that the gaseous disk vanishes at this moment, forming planet transits quickly through this mass range and the probability to detect these types of planets is reduced correspondingly. In Fig. 12 the importance of the correction of the detection biases below 20 M is only the reflection of the present observing situation for which only a limited fraction of the sample has benefited from the large enough number of HARPS measurements, required to detect small-mass Mayor et al (

7 Planet rates from RV- surveys Table 1. Occurrence frequency of stars with at least one planet in the defined region. The results for various regions of the m 2 sin i log P plane are given. Mass limits Period limit Planetary rate based on Planetary rate Comments published planets including candidates > 50 M < 10 years 13.9 ± 1.7 % 13.9 ± 1.7% Gaseous giant planets > 100 M < 10 years 9.7 ± 1.3 % 9.7 ± 1.3% Gaseous giant planets > 50 M < 11 days 0.89 ± 0.36 % 0.89 ± 0.36 % Hot gaseous giant planets Any masses < 10 years 65.2 ± 6.6 % 75.1 ± 7.4% All detectable planets with P < 10 years Any masses < 100 days 50.6 ± 7.4 % 57.1 ± 8.0% At least 1 planet with P < 100 days Any masses < 100 days 68.0 ± 11.7% 68.9 ± 11.6% F and G stars only Any masses < 100 days 41.1 ± 11.4% 52.7 ± 13.2% K stars only < 30 M < 100 days 47.9 ± 8.5 % 54.1 ± 9.1% Super-Earths and Neptune-mass planets on tight orbits < 30 M < 50 days 38.8 ± 7.1% 45.0 ± 7.8% As defined in Lovis et al. (2009) Mayor et al (

8 giant planets rates: metallicity dependence [Fe/H] = log [Fe/H] star log [Fe/H] sun from Fischer and Valenti (2005) Slide 3.11

9 mass distribu8on of RV- planets - planet mass distribution as observed by the Geneva survey - low mass planet distribution with extrapolation to number of expected planets

10 10.0 Planet rates from RV- surveys Period [days] Period distribu8on 6. Same as Fig. 5 with detection probability curves superosed. These detection probabilities are valid for the whole ple of 822 stars. After correcting for the detection bias, the tion of stars with at least one planet more massive than and with a period smaller than 10 years is estimated to be 2 %. The red points represent the planets which have been to compute the corrected occurrence rate in the box indid by the dashed line. The planets lying outside the box or g part of a system already taken into account are excluded; are shown in black. e habitable zone around the stars as being of no significance time being. This is also true for the distribution towards very masses, at any given period. An exponential extrapolation of mass distribution towards very low mass planets is not jusd if, for instance, a third, distinct population of Earth-mass ets is supposed, as suggested by Monte-Carlo simulations of et population synthesis based on the core-accretion scenario. Mordasini et al. 2009b,a). Based on the -Earth survey carried out at Keck observa-, Howard et al. (2010) have derived an estimate of the ocence rate of low-mass planets on tight orbits (apple 50 days) as l as their mass distribution. The comparison of our results he same range of parameter space with the eta-earth estie is given in Table 2. The results are also shown graphically ig. 9, where the occurrence rate is indicated for the boxes ned by Howard et al. (2010). As a result of our much larger ar sample, but also due to the better sensitivity of HARPS regard to low-mass planets, the number of detected plans significantly larger than the one issued from the Keck sur- This is specifically important for super-earths and Neptunes planets (see Fig. 2. Our estimate for the occurrence rate lanetary systems is stunningly large. Table 1 lists the estiion of the frequency of planetary systems for di erent part e m 2 sin i log P plane. We should emphasize for example 75 % of solar type stars have a planet with a period smaller 10 years. This result is limited to the domain of detectable ets, and does not involve extrapolations out of that domain. ther interesting result is obtained for the low-mass planets ight orbits: about half of solar-type stars is an host of this M2si Period [days] Fig. 7. Same as Fig. 5 but only for the HARPS subsample. The occurrence rate of planetary systems in the limited region between 3 and 100 M, and with P < 1 year, is 47 ± 7 %. Again, only the red dots and the blue triangles (candidates) have been considered for the computation of the occurrence rate. # Jupiter & cumulative rate [%] Period [days] Fig. 8. Histogram of the planet frequency for planets with masses (m 2 sin i > 50 M ). The occurrence rate for gaseous giant planets is strongly increasing with the logarithm of the period log P. Despite the significant size of our sample of 822 stars, the number of hot Jupiters is quite small (5 planets with P < 11 days). The estimated frequency, 0.9 ± 0.4% is compatible with previous estimates. (For a more complete discussion of the CORALIE-alone sample we refer to Marmier et al. (in prep). We Mayor et al (

11 Period eccentricity distribu8on From Udry & Santos 2007, Annu. Rev. Astron. Astrophys 45, 397 Slide 3.14

12 mul8- planet systems Examples for mul8- planet systems - separa8ons - masses - d min and d max Slide 3.15

13 In- class ac8vity (2) We discussed in depth what we can do and what has been done with the RV method. Now we just had a first summary what the Astrometry method can in principle do. With this information in hand, discuss in teams what science topics/questions you would like to address with astrometry and present a few of them to the class.

14 Example: HST- Astrometry of the binary GJ 1005 Hershey & Taff, 1998, AJ 116,1440 Parameters: d=6.0 pc, P=4.6yr, e=0.36, a=0.30, M 1 =0.18 M ʘ, M 2 =0.11M ʘ Slide 3.16

15 Astrometry with GAIA Satellite hardware overview Slide 3.18

16 PSR B pulsar planets Timing of the deviations of pulse arrival times (in µs) from a linear law - observations - fit for a 3 planet system - there are some long term trends at the 20 µs level and noise on the 10 µs level (from Konacki & Wolszczan 2003) Slide 3.20

17 Transit 8ming varia8ons for KOI transit model (lines) and - data points of 14 transits - timing variations are ±1 hr Periods of planets: days for transiting planet - 57 days for unseen planet (Nesvorny et al. 2012, Science 336, 1133) Slide 3.21

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