# 51Peg

After installing **kima**, we'll go through one of the examples
to start playing with the package. Let's find 51 Peg *b*!

51 Peg *b* was the first exoplanet discovered around a solar-type star. The
original paper, by Mayor & Queloz
(1995), used data from the ELODIE
spectrograph. Here we will use another dataset, obtained with the Hamilton
echelle spectrograph, situated in the Lick Observatory, in California (see
Butler et al. 2006).

Let's import the package and the example

```
import kima
from kima.examples import _51Peg
```

The name `_51Peg`

is a bit weird simply because Python variable names cannot start with a number. 🤷

To take a quick look at the RV data, let's call the `_51Peg`

function to just
build the model, without running it:

```
model = _51Peg()
model.data.plot();
```

The data consist of 256 observations over almost 6 years, from October 1995 to October 2001. Our goal is to fit a Keplerian model to these radial-velocity observations. We will assumme the number of Keplerians to be free, with a uniform prior between 0 and 1, while all other priors take default values.

We could run this model using the `kima.run()`

function, but let's use the
example directly (which runs 5000 steps by default):

```
model, res = _51Peg(run=True, load=True)
```

log(Z) = -907.1448171972309 Information = 33.55284794677641 nats. Effective sample size = 534.6495957420269

100%|██████████| 534/534 [00:00<00:00, 9019.79it/s]

We also loaded the results into the `res`

variable, which we can use to look at
some posterior distributions.

For example, the posterior for the number of planet is quite clear, showing the significant detection of the planet:

```
res.plot_posterior_np();
```

Np probability ratios: []

The orbital period is also very well constrained:

```
res.plot_posterior_periods(show_prior=True);
```

The plot above also shows samples from the prior distribution, which is log-uniform extending from 1 day to the timespan of the data.

We can also plot the histograms of the posteriors for the systemic velocity and for the instrumental jitter

```
res.hist_vsys();
res.hist_jitter();
```

and the (more interesting) phase plot using the maximum likelihood solution

```
p = res.maximum_likelihood_sample()
```

Sample with the highest likelihood value (logL = -869.59) -> might not be representative of the full posterior distribution jitter: [2.8930339] number of planets: 1 orbital parameters: P K M0 e w 4.23073 55.93763 5.07937 0.01090 0.61465 vsys: -1.78331207

```
res.phase_plot(p);
```

So, **kima** tells us that a planet at a period of 4.23 days and an amplitude of
~56 m/s is the best model given the RV data. If it was 1995, we'd be going about
changing the history of astronomy!