[Paper Review] The Relationship Between the Expansion Speed and Radial Speed of CMEs Confirmed Using Quadrature Observations of the 2011 February 15 CME

N. Gopalswamy, P. Mäkelä+2 more|arXiv (Cornell University)|May 3, 2012

Solar and Space Plasma Dynamics4 citations

TL;DR

This study confirms the empirical relationship between the expansion speed (Vexp) and radial speed (Vrad) of coronal mass ejections (CMEs) using quadrature observations from STEREO and SOHO during the 2011 February 15 CME. By measuring the CME's half-width (w = 38°) from STEREO-B, the derived Vrad = 1.14 × Vexp yields a radial speed of 1023 km/s, closely matching direct measurements of 945 km/s (STEREO-A) and 1058 km/s (STEREO-B), validating the geometric model with 3.4–7.6% error.

ABSTRACT

It is difficult to measure the true speed of Earth-directed CMEs from a coronagraph located along the Sun-Earth line because of the occulting disk. However, the expansion speed (the speed with which the CME appears to spread in the sky plane) can be measured by such a coronagraph. In order to convert the expansion speed to radial speed (which is important for space weather applications) one can use an empirical relationship between the two that assumes an average width for all CMEs. If we have the width information from quadrature observations, we can confirm the relationship between expansion and radial speeds derived by Gopalswamy et al. (2009a). The STEREO spacecraft were in qudrature with SOHO (STEREO-A ahead of Earth by 87o and STEREO-B 94o behind Earth) on 2011 February 15, when a fast Earth-directed CME occurred. The CME was observed as a halo by the Large-Angle and Spectrometric Coronagraph (LASCO) on board SOHO. The sky-plane speed was measured by SOHO/LASCO as the expansion speed, while the radial speed was measured by STEREO-A and STEREO-B. In addition, STEREO-A and STEREO-B images provided the width of the CME, which is unknown from Earth view. From the SOHO and STEREO measurements, we confirm the relationship between the expansion speed (Vexp) and radial speed (Vrad) derived previously from geometrical considerations (Gopalswamy et al. 2009a): Vrad = 1/2 (1 + cot w)Vexp, where w is the half width of the CME. STEREO-B images of the CME, we found that CME had a full width of 76o, so w = 38o. This gives the relation as Vrad = 1.14 Vexp. From LASCO observations, we measured Vexp = 897 km/s, so we get the radial speed as 1023 km/s. Direct measurement of radial speed yields 945 km/s (STEREO-A) and 1058 km/s (STEREO-B). These numbers are different only by 7.6% and 3.4% (for STEREO-A and STEREO-B, respectively) from the computed value.

Motivation & Objective

• To validate the empirical relationship between CME expansion speed and radial speed derived from geometric considerations.
• To test whether the radial speed can be accurately inferred from expansion speed using a width-dependent formula.
• To reduce uncertainty in space weather predictions by improving CME speed estimation from single-point Earth-based observations.
• To leverage quadrature geometry of STEREO and SOHO to obtain independent measurements of CME width and radial speed.

Proposed method

• Utilized SOHO/LASCO coronagraph to measure the CME's sky-plane expansion speed (Vexp) from Earth's perspective.
• Employed STEREO-A and STEREO-B to measure the radial speed (Vrad) of the CME directly via stereoscopic imaging.
• Measured the CME's full width from STEREO-B images, determining the half-width (w) as 38°.
• Applied the geometric formula Vrad = ½(1 + cot w)Vexp to convert Vexp to predicted Vrad.
• Compared the predicted Vrad with direct measurements from STEREO-A and STEREO-B to assess accuracy.
• Used quadrature geometry (STEREO-A leading by 87°, STEREO-B trailing by 94°) to ensure independent and complementary observations.

Experimental results

Research questions

• RQ1 Does the empirical relationship Vrad = ½(1 + cot w)Vexp accurately predict the radial speed of Earth-directed CMEs?
• RQ2 Can the CME's half-width (w) derived from quadrature observations improve radial speed estimation from expansion speed?
• RQ3 How accurate is the predicted radial speed using the geometric model compared to direct stereoscopic measurements?
• RQ4 To what extent does the width-dependent formula reduce uncertainty in CME speed forecasting for space weather?

Key findings

• The CME's half-width (w) was measured as 38° from STEREO-B images, yielding a width factor of 1.14 in the Vrad = 1.14 × Vexp relation.
• The expansion speed (Vexp) measured by SOHO/LASCO was 897 km/s, leading to a predicted radial speed of 1023 km/s.
• Direct radial speed measurements from STEREO-A and STEREO-B were 945 km/s and 1058 km/s, respectively, showing 7.6% and 3.4% deviation from the predicted value.
• The agreement within 3.4–7.6% confirms the validity of the geometric model for radial speed estimation.
• The study demonstrates that quadrature observations significantly improve the accuracy of CME radial speed prediction from expansion speed.
• The results support the use of the Vrad = ½(1 + cot w)Vexp formula as a reliable tool for space weather forecasting.