udpate hgca tutorial discribing differences with IAD

docs/tutorials/HGCA_tutorial.ipynb

@@ -8,7 +8,15 @@
     "\n",
     "Jason Wang (2023)\n",
     "\n",
-    "We will demonstrate how to fit the stellar absolute astrometry from the [Hipparcos-Gaia Catalog of Accelerations (HGCA; Brandt 2021)](https://ui.adsabs.harvard.edu/abs/2021ApJS..254...42B/abstract) to help constrain the mass and orbital parameters of the companion. This is an alternative to fitting the Hipparcos IAD and Gaia astrometry. We encourage users to try both to see how similar or different the results are, as the two methods utilize the same underlying data. The implementation of fitting the HGCA here is based on [Brandt et al. 2019](https://ui.adsabs.harvard.edu/abs/2019AJ....158..140B/abstract), but utilizes the DR3 version of the HGCA. \n",
+    "We will demonstrate how to fit the stellar absolute astrometry from the [Hipparcos-Gaia Catalog of Accelerations (HGCA; Brandt 2021)](https://ui.adsabs.harvard.edu/abs/2021ApJS..254...42B/abstract) to help constrain the mass and orbital parameters of the companion. The implementation of fitting the HGCA here is based on [Brandt et al. 2019](https://ui.adsabs.harvard.edu/abs/2019AJ....158..140B/abstract), but utilizes the DR3 version of the HGCA. \n",
+    "\n",
+    "## Difference to fitting IAD directly\n",
+    "\n",
+    "This method is an alternative to fitting the Hipparcos IAD and Gaia astrometry. Instead of fitting the individual epochs of Hipparcos data, which also includes needing to fit for the position, proper motion, and parallax of the star, we are only fitting for two differential proper motions: the proper motion difference between Hipparcos and the change in position between Hipparcos and Gaia; the proper motion difference between Gaia and the change in position between Hipparcos and Gaia. This simplifies the fit, but also ignores any detectable curvature in the stellar astrometry seen by Hipparcos. For planet companion cases, the acceleration should be well within the noise of the Hipparcos measurements. \n",
+    "\n",
+    "The benefit of using this technique is that the errors should be more robust. The HGCA catalog inflates the error bars from the Hipparcos and Gaia measurements on a global scale to match the true observed scatter in the data. Additionally, there are bad epochs in the Hipparcos IAD that may not be removed. \n",
+    "\n",
+    "We encourage users to try both to see how similar or different the results are, as the two methods utilize the same underlying data. \n",
     "\n",
     "\n",
     "## Obtain the necessary data\n",