The figure on the left shows the number of shock waves observed from 1974 to 1985 by a pair of spacecrafts/probes (upper panel), or only by one of the spacecrafts (lower panel) as a function of the longitudinal separation (ΔΦ) between the probes. The constellations are divided in three groups according to each pair of probes: Helios 1 and 2 (black), Helios 1 and IMP-8/ISEE-3 (gray), and Helios 2 and IMP-8/ISEE-3 (white). The figure on the right shows the same results, but as percentages. 

Contexts in source publication

Context 1

... near Earth observations by IMP-8/ISEE-3 were included on the estimate, larger angles started to appear and new shock extensions were revealed. The full longitudinal range of the inner heliosphere was covered by the new points included on the observations and a new scenario for the shocks extension estimate took place. The left side of Figure 3 shows the rate of shocks for each longitudinal separation considered. In that figure, the values vary from 10 to 170 • , and each column centered in a given Φ represents the sum of all events in the interval I (Φ I < (Φ + 10 • )). This means that the number of cases centered in 20 • are a result of the number of cases in our sample where the angles were bigger than or equal to 20 • and smaller than 30 • , and consecutively for the other angles in the ...

Context 2

... it is shown in Figure 3, there are bars that are in the right side up and others that are upside down for both the plots. The former ones correspond to those events where one of the constellations (two different points in the space) had seen the same shock. So from the different constellations separated by colors -H1 and H2 (black); H1 and IMP-8 (gray); and H2 and IMP-8 (white) -, we have the total number of cases in each angular separation considered from the set of shocks under study. And the later ones represent those shock waves observed by only one of the three points of reference. As it is shown in the left side of Figure 3, increasing the angular distance between two different observational points diminishes the number of events observed by each of the constellations. In percentage, the distribution of our sample shows a clear trend that is illustrated in the right side of Figure 3. As we go to bigger angular separations, the percentage of shocks seen by both spacecrafts decreases, following a quasi-exponential decrease. Even though we have some special cases with large angles, like those events at 120 • , 130 • , and 150 • , we need to investigate them in details in order to certify that they really correspond to the same event seen in different points. According to the percentage we found in the right side of Figure 3, at ΔΦ = 90 • one has 50% of chance of seeing a shock or not seeing the same shock in two different points of ...

Context 3

... it is shown in Figure 3, there are bars that are in the right side up and others that are upside down for both the plots. The former ones correspond to those events where one of the constellations (two different points in the space) had seen the same shock. So from the different constellations separated by colors -H1 and H2 (black); H1 and IMP-8 (gray); and H2 and IMP-8 (white) -, we have the total number of cases in each angular separation considered from the set of shocks under study. And the later ones represent those shock waves observed by only one of the three points of reference. As it is shown in the left side of Figure 3, increasing the angular distance between two different observational points diminishes the number of events observed by each of the constellations. In percentage, the distribution of our sample shows a clear trend that is illustrated in the right side of Figure 3. As we go to bigger angular separations, the percentage of shocks seen by both spacecrafts decreases, following a quasi-exponential decrease. Even though we have some special cases with large angles, like those events at 120 • , 130 • , and 150 • , we need to investigate them in details in order to certify that they really correspond to the same event seen in different points. According to the percentage we found in the right side of Figure 3, at ΔΦ = 90 • one has 50% of chance of seeing a shock or not seeing the same shock in two different points of ...

Context 4

... it is shown in Figure 3, there are bars that are in the right side up and others that are upside down for both the plots. The former ones correspond to those events where one of the constellations (two different points in the space) had seen the same shock. So from the different constellations separated by colors -H1 and H2 (black); H1 and IMP-8 (gray); and H2 and IMP-8 (white) -, we have the total number of cases in each angular separation considered from the set of shocks under study. And the later ones represent those shock waves observed by only one of the three points of reference. As it is shown in the left side of Figure 3, increasing the angular distance between two different observational points diminishes the number of events observed by each of the constellations. In percentage, the distribution of our sample shows a clear trend that is illustrated in the right side of Figure 3. As we go to bigger angular separations, the percentage of shocks seen by both spacecrafts decreases, following a quasi-exponential decrease. Even though we have some special cases with large angles, like those events at 120 • , 130 • , and 150 • , we need to investigate them in details in order to certify that they really correspond to the same event seen in different points. According to the percentage we found in the right side of Figure 3, at ΔΦ = 90 • one has 50% of chance of seeing a shock or not seeing the same shock in two different points of ...

Context 5

... it is shown in Figure 3, there are bars that are in the right side up and others that are upside down for both the plots. The former ones correspond to those events where one of the constellations (two different points in the space) had seen the same shock. So from the different constellations separated by colors -H1 and H2 (black); H1 and IMP-8 (gray); and H2 and IMP-8 (white) -, we have the total number of cases in each angular separation considered from the set of shocks under study. And the later ones represent those shock waves observed by only one of the three points of reference. As it is shown in the left side of Figure 3, increasing the angular distance between two different observational points diminishes the number of events observed by each of the constellations. In percentage, the distribution of our sample shows a clear trend that is illustrated in the right side of Figure 3. As we go to bigger angular separations, the percentage of shocks seen by both spacecrafts decreases, following a quasi-exponential decrease. Even though we have some special cases with large angles, like those events at 120 • , 130 • , and 150 • , we need to investigate them in details in order to certify that they really correspond to the same event seen in different points. According to the percentage we found in the right side of Figure 3, at ΔΦ = 90 • one has 50% of chance of seeing a shock or not seeing the same shock in two different points of ...

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... have studied shock angular extension in the inner heliosphere using observations from H1, H2, and IMP-8/ISEE-3 spacecrafts. By using a pair of these probes each time, we found that shock extension decreases as the probes angular separation increases. When a CME is observed at the solar limb, for example, there is 50% of probability of seeing Figure 4. This is the same plot as shown before in the percentage of shocks (upper panel of Figure 3). The error margin for the percentage of shock observed by multi-points into each longitudinal separation as seen by Helios-1,2 and IMP-8/ISEE-3. As one goes further in degrees, the uncertainty for observing a shock in the angular separation (ΔΦ) increases. Observe that in ΔΦ = 110 • the biggest error for our estimate is found. That is because only two events (left side in Figure 3) were registered for that angle: one was detected by a pair of probes, and the other, by a single probe. the shock driven by the ICME at Earth. Further investigation is needed to evaluate those cases with large (> 110 • ) ...

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... have studied shock angular extension in the inner heliosphere using observations from H1, H2, and IMP-8/ISEE-3 spacecrafts. By using a pair of these probes each time, we found that shock extension decreases as the probes angular separation increases. When a CME is observed at the solar limb, for example, there is 50% of probability of seeing Figure 4. This is the same plot as shown before in the percentage of shocks (upper panel of Figure 3). The error margin for the percentage of shock observed by multi-points into each longitudinal separation as seen by Helios-1,2 and IMP-8/ISEE-3. As one goes further in degrees, the uncertainty for observing a shock in the angular separation (ΔΦ) increases. Observe that in ΔΦ = 110 • the biggest error for our estimate is found. That is because only two events (left side in Figure 3) were registered for that angle: one was detected by a pair of probes, and the other, by a single probe. the shock driven by the ICME at Earth. Further investigation is needed to evaluate those cases with large (> 110 • ) ...

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... critical interval for the percentage of shocks (right side of Figure 3) was determined by using the test of proportions analysis (for details, see Kalbfleisch 1979). Figure 4 shows the error bars that represent a 95% confidence intervals for each angular separation. The estimated value is more accurate as we have a larger number of cases from the sample, like it is shown in Figure 4. A critical value at ΔΦ = 110 • is found as we have just two cases inside this angular ...