RITMO ONTOLÓGICO

Young (<1 Gyr), early type M dwarfs typically have rotation periodsProt<5 days (Mamajek & Hillenbrand 2008). We have thus focused our analysis on the identification of SBK2 stars with these fast rotation rates.

Figure 2.8 Comparison of Lomb Scargle to ACF+FFT rotation periods. The black, solid line represents perfect agreement. We find that the rotation periods calculated using the ACF+FFT routine are underestimated by 26%, and we correct our derived results by this amount.

Section 2.2, with the FFT identifying regular peaks in the ACF corresponding to a recurrent signal and its aliases, and with individual fits to these peaks used to compute the associated stellar rotation period and assess the quality of the identification. This combined ACF and FFT algorithm identified 1,113 candidate fast rotators out of the 58,484 SUPERBLINK stars monitored inK2 campaigns 0-15. The complete list of SBK2 targets identified as fast rotators can be found in the table presented in Appendix A.

Figure 2.9 shows a histogram of the distribution of candidate fast rotators as a function of their estimated rotation period, Prot. The number of detected fast rotators decreases at the rotation period increases, with most objects having estimated rotation periodsProt<1.5 days. This distribution most probably reflects the true statistics of fast rotators, as defined by the physical mechanisms responsible for their slow down. However, the distribution could

Figure 2.9 Distribution of the rotation periods identified in this work. We find fewer targets with with Prot >1.5 days. This may be intrinsic to the population of young stars we study here or a systematic trend in the data.

be affected by a number of selection biases. For example, slower rotators have a weaker dynamo effect and are thus likely to have smaller spots. As a result their star spot modulation would have lower intrinsic amplitudes, which would make them harder to identify amidst the instrumental noise. If this is true, then the identification of stars with rotation periods Prot & 2 days might therefore be a significant challenge using K2 data. In future work we would would like to develop an algorithm that can identify additional stars with rotation periods Prot > 2 days, and especially stars with Prot > 5 days, which were not included in the present study.

Figures 2.10 - 2.13 presents the light curves of several of these fast rotators. In each subplot, the top panel shows the first half of the light curves while the bottom panel shows the second half of the light curve (typically 40 days). Each y-axis has been scaled to 3x the

light curve amplitude.

Figure 2.10 presents three of the fastest rotators on the left. Their rotation periods vary form 7-21 hours. We note that both the amplitude and shape of the light curve changes over the course of the K2 observations. This is likely due to the change in number and location of the spots on the photosphere. The right half of the figure presents three of the slowest rotators in our sample of fast rotators. Their rotation periods vary from 3-4 days. Compared to the slow rotators, both the shape and pattern of modulation is more consistent during the campaign. We believe this pattern stability is in an indication that spots are longer lived on slower rotators.

Figure 2.10 Three examples of the fastest rotators (left) and slowest rotators (right) in our subset of stars with rotation periods <3.5 days.

We see small differences in the patterns between stars of different colors, which is also a proxy for mass. Blue stars are main-sequence stars more massive than the Sun, while red stars are less massive than the Sun, see Table 2.2. We utilize theGAIAG magnitude introduced in Chapter 1 as well as the 2MASS J magnitudes. The Two Micron All-Sky Survey (2MASS) was an all sky survey in the infrared conducted jointly by the University of Massachusetts and NASA.3 _{The J bandpass peaks at a wavelength of 1.235µm. Figure 2.11 presents three}

of the reddest rotators on the left (3.0<G-J<3.7) and three of the bluest rotators on the right (0.3<G-J<0.8) 4 The amplitude of modulation for the red rotators is ∼ 5% in each case while the blue rotators have an amplitude of modulation <1%. This could mean that the bluer (more massive) rotators are intrinsically less spotted, either because they have fewer spots overall, or because their spots are smaller. An alternate explanation is that the contrast between the spots and the photosphere are sharper in the less massive/cooler stars that it is in the more massive/hotter ones. This may happen if the temperature difference between the spots and the photosphere is larger in the cooler stars. This higher contrast would cause a higher level of modulation for red rotators compared to blue rotators.

Table 2.2: Color to Mass Conversion

G-J Mass 1-1.2 F 1.2 - 1.3 G 1.3 - 1.8 K > 1.8 M ∼2.8 Full Convection 3_{https://irsa.ipac.caltech.edu/Missions/2mass.html}

4_{Eric Mamajek determined FGKM spectral types corresponding to G-J colors to be: F 1-1.2, G}

1.2 -1.3, K 1.3-1.8, and M > 1.8. Full convection begins at M4.5 or G-J = 2.8. See his table at

Figure 2.11 Three examples of the reddest fast rotators (left) and bluest fast rotators (right). Figure 2.12 presents the light curves of three detected fast rotators with some of the lowest amplitude of modulation compared to three stars with the highest amplitude. The stars with the lowest amplitudes show variability on the order of 0.5% while the stars with the highest amplitudes show variations on the order of 4%. There does not seem to be any obvious correlation between the amplitude of modulation and the rotation rate. Instead, we believe that the amplitude of modulation is related to the color of the stars as noted above, see Figure 2.11. This idea is explored further in Chapter 5.

In Figure 2.13, we present three of the brightest (5.8<G<7.5) fast rotators compared to three of the faintest fast rotators (18.4<G<20.4), to show that the brightness of a star has

Figure 2.12 Three examples of fast rotators with the lowest amplitude of variability (left) and highest amplitude of variability (right).

no effect on our ability to identify rotation modulations. We do observe that fainter stars appear to show higher amplitudes in their rotation modulations on average. This however is not a selection effect, but simply the fact that the fainter stars in our program are also redder since the are dominated by low-mass M dwarfs, while the brighter stars are largely FGK stars, see Figure 3.1. As it turns out, M dwarf fast-rotators tend to show larger spots on their surface and thus have larger amplitudes in their modulation, while fast-rotating FGK stars generally show smaller spots and thus have lower amplitudes in their rotation modulations.

Figure 2.13 Three examples of the brightest fast rotators (left) and dimmest (right).

the apparent GAIA G magnitudes throughout this study. The G band is a broad optical bandpass (320-1100nm). The trend in Figure 2.14 indicates an increase in the detection of fast rotators when one observes fainter magnitudes, which is counterintuitive because one would expect rotation modulations to be harder to detect in fainter stars. However, this likely occurs because again the fainter targets are comprised mainly of low-mass M dwarfs, while the brighter targets are largely more massive FGK dwarfs (see Figure 6.1). The age- activity relationship presented by West et al. (2008) indicates that M stars remain active longer than the more massive FGK stars. Therefore, late-type M stars will persist as rapid rotators longer than bluer, early type stars, making it it more likely to find a rapid rotator

Figure 2.14 Fraction of rapidly rotating M dwarfs as a function of magnitude. At fainter magnitudes, the fraction of fast rotators increases because the fainter magnitudes are com- prised mainly of M dwarfs as indicated by Figure 3.1. The drop off at G>16 is indicative of the K2 detection limit for fast rotators. This limit is due to light curves that are too noisy to detect a repeating signal.

in a sample dominated by M dwarfs, like this subset of faint stars.

Interestingly, the trend in Figure 2.14 reveals a sharp downturn at G>16, which suggests that G > 16 is the magnitude limit for detecting modulations from spots in K2 data. This limit could due to 1) the K2 light curves becoming too noisy to detect a repeating signal or 2) fainter stars being genuinely less likely to show rotational modulation. Figure 2.15 is a frequency histogram of the SBK2 sample (black) and the fast rotator subsample (red). As the histogram indicates, the majority of the stars in these samples are brighter than 16th magnitude. The downturn however occurs earlier for fast rotators that for the slower rotators. However, another interesting feature of this histogram is the bimodal distribution

Figure 2.15 Frequency histogram of apparent G magnitudes of all SBK2 stars (black) and rapid rotators (red). These histograms indicate that the downturn in detection of rapid rotators with G > 17 is a result of our sample becoming incomplete at this magnitude and not a limitation of our detection methods. We also note the bimodal distribution of fast rotators.

of the fast rotators. We find the fast rotators to show two peaks, one at G∼9 and another one at G∼15. This suggests some hidden trend in the distribution of fast rotators. The brighter peak at G∼9 likely occurs because most of the brighter stars in our sample are F stars. These F type stars, according to gyrochronology, are genuinely more likely to be fast rotators than stars of lower mass, because they decelerate slower than less massive objects (GK dwarfs).

To verify this, we plot the rotation rate as a function of the star’s color in Figure 2.16. The G-J color is used. The figure indicates that fast rotators tend to fall into two groups: blue stars, with colors consistent with spectral type F, and red stars, with colors consistent

with fully convective M dwarfs.This is evidence that red (M) dwarfs persist as rapid rotators for longer than more massive stars. The clustering of rapid rotators at P=2 days and G-J = 1.0 are likely the more massive members of the Hyades and Pleiades. This topic will be discussed further in Chapter 4.

Figure 2.16 Rotation period as a function of color.

A second way to view the above mentioned bias in our selection methods is in a color-

apparent magnitude diagram, see Figure 2.17. This figure plots all the SBK2 stars in black with the fast rotators overplotted in red. The figure shows a distribution similar to that of an HR diagram, with the main sequence cutting across from upper-left to lower-right. Because our sample is a high-proper motion selected subset, most stars tend to have relatively close distance, and their apparent magnitudes are correlated with their absolute magnitude. What is more interesting is that we clearly see the two groups of stars: blue F stars at apparent

magnitude G∼9, and red M dwarfs at apparent magnitude G∼16. Therefore the bimodal distribution in the apparent magnitude distribution simply reflects the color dependence of the variability. The stars with the faintest magnitudes (G>18) are in fact K stars of intermediate colors (G-J∼2), not expected to be fast rotators. This explains the dowturn at G>17 noted in Figure 2.14. Actually, we will show in the next section that these faint stars are in fact members of the Galactic halo, and are not fast rotators because they are much older.

Figure 2.17 Color-apparent magnitude of all SBK2 stars (black) and fast rotators (red). FGKM spectral types correspond to G-J colors of: F 1-1.2, G 1.2 -1.3, K 1.3-1.8, and M > 1.8. This plot shows that the majority of the stars in our sample are brighter than G=16, and that we detect very few stars fainter than 18th magnitude. We conclude that the trend seen in Figure 2.14 is due to the incomplete nature of the sample at faint magnitudes and is not a reflection of the sensitivity of our rotation period finding algorithm.

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