As discussed in Section 2.1.5, stellar jitter is well known to increase with stellar rotation. With very young stars, it can be difficult to distinguish between activity induced RV vari- ability, and RV variability induced by an orbiting companion. In this section, we consider three metrics to assess the magnitude and potential cause of RV variability in these young stars.
The projected rotational velocity, vsini, provides a useful minimum value for the stellar rotation rate, and is measured uniformly for all stars in our sample. For each star, we compare thevsini value with RV dispersion, defined as the standard deviation of the epoch RVs, to determine an empirical estimate of the expected activity induced variability. Objects that show a higher than average standard deviation for a given vsinimay have an additional component to their variability, such as the reflex motion from a companion. In Figure 3.4, we plot the RV dispersion versus the fitted vsini values for the young stars in the sample along with star names for stars with large RV dispersions with the exception of two objects, RXJ1548.9-3045 and V1096 Tau; their dispersions lie far above this plotting region at 20.3 km/s and 9.7 km/s respectively. These two are newly discovered spectroscopic binaries and are discussed in Section 3.6, and will not be included in the following discussion on identifying variability. RV dispersions for all stars are listed in Table 3.4.
Figure 3.4 Here we plot the RV dispersion, defined as the standard deviation of the epoch RVs (m/s), versusvsinifor Upper Scorpius (solid circles) and Taurus-Auriga (solid squares). Stars with large dispersions are labeled. A histogram with a bin size of 50 m/s is shown to the right with Taurus-Auriga in open boxes and Upper-Sco in crosshatched boxes.
Figure 3.4 shows a pronounced difference in the RV distributions of dispersions of Upper- Sco stars at∼10 Myr and Taurus-Auriga stars at∼1-2 Myr. Consequently, we discuss these samples separately. Taurus-Auriga stars (24, solid squares) have wide range of RV dispersion values between 75-584 m/s with an average of 296 m/s andvsinifit values between 4-52 km/s
with an average of 14 km/s. It is worth noting that for the Taurus-Auriga sample that while there is a large range in RV dispersion values for slowly rotating stars (vsini ≤ 15 km/s), all rapidly rotating stars show large (≥360 m/s) RV dispersions. The correlation of rotation and chromospheric induced RV variably appears to exist even at this young age. Overall, because of the large range in RV dispersions of the Taurus-Auriga stars, it is not possible to identify any of the most RV variable stars as having a orbiting companions.
The Upper-Sco stars (13, solid circles) have a range of RV dispersions between 41-561 m/s with an average of 161 m/s and vsini fit values that range from 4-18 km/s with an average of 10 km/s. Only RXJ1540.9-3024, a candidate RV variable to be discussed in Section 3.5, stands out as an outlier with an average RV dispersion of 561 m/s. Treating RXJ1540.9- 3024 as an outlier, the remaining 12 stars in Upper-Sco have a much smaller range in RV dispersions than Taurus-Auriga with RV dispersions between 41-182 m/s with an average of 127 m/s. Our RV standards have RV dispersions between 75-115 m/s with an average of 114 m/s. This is roughly two times worse empirical precision than that achieved by the same technique on Gemini Phoenix and VLT CRIRES in 2.
To determine how statistically significant the RV dispersions are, we compute a second metric we call ∆, in Equation 3.5, defined as the RV dispersion divided by the average error (< σEpoch >) and listed in Table 3.4. In Figure 3.5 we plot ∆ vs vsini for each object in Taurus-Auriga (solid squares) and Upper-Sco (solid circles). Taurus-Auriga stars show a large spread in ∆ values between 1.5-19.3 with an average value of 9.4 and a standard deviation of 4.8. With this metric, we still see no evidence for the RV variability being
caused by an orbiting companion. For Upper-Sco stars, excluding RXJ 1540.9-3024, there is a concentration of ∆ values objects between 0.9-5.1 with an average value of 3.2 and a standard deviation of 1.1. RXJ 1540.9-3024 has a ∆ value of 12.4, implying that the large RV dispersion for this star is not a consequence of large RV errors. Our RV standards had ∆ values between 3.3-6.1 with an average value of 4.4.
∆ = RV Dispersion
< σEpoch1, σEpoch2, ...σEpochN >
Figure 3.5 Here we plot the standard deviation of the epoch RV’s divided by the error versus
vsinifor Upper Scorpius (solid circles) and Taurus-Auriga (solid squares). A histogram with a bin size of 2 is shown to the right. Taurus-Auriga stars are in open boxes and Upper-Sco stars are in crosshatched boxes.
Table 3.4: RV Dispersions - Keck/NIRSPEC
RV Mean Error Star Dispersion < σEpoch > ∆
m/s m/s
Young Stars - Taurus-Auriga
V1306 Tau(RXJ0409.8) 93 30 3.2 V1096 Tau 9724 28 347.6 FN Tau 332 31 10.6 CY Tau 243 28 8.7 CIDA 3 567 38 14.9 V410 X-ray 7 376 25 15.0 IP Tau 229 26 8.9 KPNO-Tau 13 399 28 14.2 DH Tau 215 29 7.4 IQ Tau 584 30 19.3 JH 56 241 28 8.6 J1-665 409 31 13.1 V1321 Tau(RXJ0432.8) 324 33 9.8 DM Tau 240 43 5.6 JH 108 215 35 6.2 DN Tau 93 43 2.2 RXJ0437.4+1851 A 130 32 4.1 RXJ0437.4+1851 B 158 32 5.0 RXJ0438.2+2303 75 50 1.5 CoKu Tau 4 365 33 11.1 GM Aur 344 31 11.2 V1353 Tau(RXJ0457.0) 240 37 6.5
Table 3.4: RV Dispersions - Keck/NIRSPEC
RV Mean Error Star Dispersion < σEpoch > ∆
m/s m/s
CIDA 8 531 31 17.2
CIDA 10 405 35 11.7
Young Stars - Upper Scorpius
RXJ1534.3-3300 155 46 3.4 RXJ1540.9-3024 1055 47 22.5 RXJ1546.0-2920 102 37 2.8 RXJ1546.7-3210 167 58 2.9 RXJ1548.9-3045 20276 52 386.6 RXJ1551.1-2402 97 31 3.1 RXJ1552.5-2633 157 31 5.1 RXJ1557.8-2305 41 44 0.9 RXJ1558.8-2512 125 44 2.8 RXJ1605.6-2152 132 32 4.1 RXJ1607.0-2043 105 37 2.8 ScoPMS 14 182 52 3.5 ScoPMS 32 110 48 2.3 ScoPMS 42 B 156 36 4.4
Radial Velocity Standards
Table 3.4: RV Dispersions - Keck/NIRSPEC
RV Mean Error Star Dispersion < σEpoch > ∆
m/s m/s GJ 382 111 28 4.0 GJ 628 159 37 4.3 GJ 725 A 75 22 3.3 GJ 725 B 109 28 3.9 GJ 876 115 24 4.9
The third metric we consider is the P-χ2 test. A P-χ2 test shows how significant a set of observations deviates from an expected χ2 distribution (Carney et al. 2003). In our
implementation, it indicates how significant the epoch RV varies from the average RV given the calculated error and the number of epochs. We use Equation 3.6 in calculating our χ2
values, where RVEpoch is the epoch RV, RV? is the average RV for all epochs, and σEpoch is the epoch error as described in Section 3.2.1. A p-value of 0.01 would indicate a 99% confidence that a star has significant RV variability over the observational period.
χ2 =
X
(RVEpoch−RV?)2
σ2
Epoch
(3.6)
In Figure 3.6 we show histograms for of p-values from our P-χ2 test are plotted for
Taurus-Auriga (open boxes) and Upper-Sco (crosshatched boxes). We can see that these two populations are quite different. The ensemble of Upper-Sco stars exhibit a flat distribution
between zero and one. This is consistent with a population of RV non-variable stars. The two exceptions in Upper-Sco are RXJ1548.9-3045 and RXJ1540.9-3024, with p-values of
<<0.0001 and 2.2×10−25 respectively. Taurus-Auriga stars, on the other hand, show a
higher fraction of low p-values with 16 out of 24 stars having a p-values less than 0.01. Our RV standards have values between 0.24-1 with an average value of 0.73.
Figure 3.6 A histogram of the p-values from our P-χ2test on 24 Taurus-Auriga and 12 Upper-
Sco (crosshatch) stars are shown here. Stars with p-values less than 0.01 have statistically significant deviation from the expectedχ2distribution. This signals that they have significant RV variability.
Using all three metrics, a large fraction of stars in Taurus-Auriga stars exhibit evidence of having statistically significant RV variability. However, since we do not expect the majority of these stars to have hot Jupiter-like companions, we interpret this as indicating that many
Taurus-Auriga stars have large amplitude stellar induced RV variations. Consequently, we do not identify any of these stars as candidate planet hosts, however, in Section 4.0.2 we investigate identifying planets in the presence of spots.
For Upper-Sco stars, all three metrics identify only RXJ1540.9-3024 as an RV variable with an amplitude unlike the remainder of Upper-Sco stars. We classify RXJ1540.9-3045 as a candidate planet host.