- Email: [email protected]
HSUNSPOTS: A tool for the analysis of historical sunspot drawings
Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
Contents lists available at ScienceDirect
Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
HSUNSPOTS: A tool for the analysis of historical sunspot drawings A. Cristo a, J.M. Vaquero b,n, F. Sa´nchez-Bajo c a b c
´ceres, Spain Departamento de Tecnologı´a de los Computadores y de las Comunicaciones, Escuela Polite´cnica, Universidad de Extremadura, Avda de la Universidad s/n, 10071 Ca ´ceres, Spain Departamento de Fı´sica Aplicada, Escuela Polite´cnica, Universidad de Extremadura, Avda de la Universidad s/n, 10071 Ca Departamento de Fı´sica Aplicada, Escuela de Ingenierı´as Industriales, Universidad de Extremadura, Avda de Elvas s/n, 06071 Badajoz, Spain
a r t i c l e in fo
abstract
Article history: Accepted 28 December 2009 Available online 6 January 2010
Valuable information about the evolution of solar activity is recorded in early sunspot drawings, especially during 17th–19th centuries. In this context, we have developed a computer program to analyze historical drawings showing the trajectories of sunspots across the solar disk. As an example, we have analysed the drawings published in the book De heliometri structura et usu by Zucconi (1760). These drawings span the period from April 1754 to June 1760. We present the Butterfly diagram for those years. The ending of solar cycle 0 and the beginning of solar cycle 1 are clearly noted in this diagram. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Software Sunspots drawings 18th century data Butterfly diagram
1. Introduction Early drawings of sunspots (from the beginning of the 17th century) have been extensively used to characterize solar activity during past centuries, extending the series of sunspot numbers back into the past (Vaquero and Va´zquez, 2009). In this regard, studies of the solar activity based on the analysis of early sunspot observations are very important, owing to the intimate connection between the activity of the sun and the terrestrial climate. Moreover, these drawings can be also used to measure the position of sunspots and estimate the solar rotation rate by analyzing the changes in the position of the sunspots with time. In this regard, note that the only information on surface rotation during these centuries comes from contemporary drawings of the Sun including sunspots (Casas et al., 2006). In this way, note also that accurate and continuous records of the positions of the sunspots, used for determining the solar rotation rate, are only available for solar cycles since last decades of the 19th century (Royal Greenwich Observatory, 1980; Balthasar et al., 1986). The studies of solar rotation based on historical drawings of sunspots are important because of the link between solar activity and the solar dynamo (Tobias, 2009). In this regard, for example, some work has been performed using drawings from the so-called Maunder Minimum ( 1645 to 1715). Some of these studies suggest that solar rotation was more differential during the Maunder Minimum than at the present time (Eddy et al., 1976; Ribes et al., 1987; Vaquero et al., 2002). However, historical drawings useful for the measurement of solar rotation are sparse.
n
Corresponding author. Tel.: + 34 676 618 160; fax: + 34 924 289 651. E-mail addresses: [email protected] (A. Cristo), [email protected] (J.M. Vaquero), [email protected] (F. Sa´nchez-Bajo). 1364-6826/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2009.12.010
For this reason, the search and analysis of historical solar drawings to determine sunspot positions is an interesting task (Arlt, 2008, 2009). The analysis of ancient solar drawings can be performed manually, by measuring the number and positions of the identifiable sunspots on each drawing, one by one, and transforming subsequently these positions to heliographic coordinates by standard methods (Beck et al., 1995; Roy and Clarke, 1989; Smart, 1977). However, this is a tedious task that could be shortened by using an automatic procedure. For this reason, we present here HSUNSPOTS, a software tool developed for analyzing solar drawings, which can be employed in the study of ancient solar records. In the following sections we describe, first, the software, and, next, as an example, we use it to analyze the solar drawings prepared by Zucconi (1760).
2. Description of the software The program HSUNSPOTS is a windows-based computer tool especially developed to register, in an automatic way, the positions and areas of sunspots in solar drawings. It is intended for both historians of astronomy and solar physicists. This software has been developed over a C++ environment and runs under all Microsoft Windows platforms and will be available for GNU Linux operating systems soon. The low size of the application (about 1.2 MB) makes it very suitable for easy distribution. HSUNSPOTS is based on the creation of user projects, which store information (including contact information) about the observer or analyzer and the location of the place of the daily observations. For each project, a sequence of observations can be
188
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
Fig. 1. A sunspot drawing by Zucconi (upper panel) analysed with HSUNSPOTS software (lower panel).
managed by just loading an image of the Sun on the desired day and marking with a click of the mouse, in a very intuitive way, the sunspots present in the picture. The file storing a user project follows a structure designed for the application, and it is completely interchangeable. In this way, an observer can distribute his project file to others to consult his observations or to complete with the other observer’s data. In the near future, the application will be improved to be able to merge several users’ projects (in order to distribute the observation work among different authors), or to export read only projects, for a safer distribution and publication. It is possible to carry out several operations on the marked information, such as grouping the sunspots and labelling them to track the trajectory of these sunspots or groups over the solar disk; estimating the total sunspot area (which is related to solar activity); and showing the results in different kinds of charts. The application has been divided into four main windows.
template representing the state of the Sun (L0, B0, P angles and apparent diameter1). All the solar ephemeris information is firstly automatically calculated by transforming the observation date inserted by the user to the corresponding Julian Day, according to the expressions and tables detailed in Chapter 10 of Meeus (1998), and later using the Julian Day to automatically calculate the Sun’s L0, B0, P angles and apparent diameter according to the expressions detailed in the Chapter 29 of the same book. In this regard, we have adopted the convention of placing the east limb (E) to the right and the west limb (W) to the left, in opposite of the other convention used (Phillips, 1992). When all the ephemeris have been calculated and the user has placed the image over the template, then it is possible to select, with a mouse click, the sunspots visible in the drawing. In this regard, the measurement of data such as the position and relative area of the sunspots is carried out in an automatic way by the program (using the auxiliary data L0, B0 and P for the date of the observation, previously calculated) and stored for use in subsequent windows.
2.1. Analysis window This is the main option window (Fig. 1). It allows the user to load an image of the Sun, move it, rotate it, resize it and/or change its opacity in order to adjust the solar limb to a predefined
1 L0 and B0 are, respectively, the heliographic longitude and latitude of the centre of the solar disk. P is the position angle of the northern extremity of the axis of rotation, measured eastwards from the North Point of the solar disk.
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
2.2. Viewing/editing window This window allows the user to display the data of the groups and sunspots analysed in the previous window (heliographic coordinates, relative areas and hemisphere where they are located), and edit them. The groups and spots analysed are also shown graphically in this window. 2.3. Tracking window In this window, the labelled groups and sunspots are displayed in order to analyze their temporal behaviour and their trajectories over the solar disk. 2.4. Statistics window In this window it is possible, using various charts, to display different parameters of the labelled data, such as the total area or number (by hemisphere, if required) of the groups and sunspots, along with the time period of the observations.
3. An example: Zucconi’s drawings A set of early sunspot drawings was published by Zucconi (1760), showing the path across the solar disk of some spots observed
189
during the period from April 1754–June 1760. Fig. 2 shows, as an example, six sunspot drawings published by Zucconi (1760) although the complete set includes 38 drawings. Information about a precise date and time for all the drawings is provided by Zucconi (1760). HSUNSPOTS was used to estimate the position of all the recorded sunspots (1202 in total, involving about 60 sunspot groups) on different observation days. In these drawings, the sunspots show fine details, although the quality of the alignment of the sunspots and the cardinal directions is not ideal. It is possible to see, the E/W coordinates of the Sun’s limb are the opposite in the application regarding the Zucconi’s drawings. Because of this, it was necessary to flip all the drawings horizontally before analyzing them with the program. In the next version advanced image transformations will be available, such as horizontal and vertical flipping and rotation. After analyzing the flipped Zucconi’s drawings, using the estimated sunspot positions calculated automatically by the application, a Butterfly diagram (Fig. 3, lower panel) that spans the period 1754–1760 has been generated. We have included both Wolf and Group Sunspot Number in Fig. 3 (upper panel). Butterfly diagram is compatible with the actual (and poor) knowledge of solar activity during these years. At the beginning of the diagram, where the number of observations is higher, the ending of solar cycle 0 is noticeable, with sunspots located at very low heliographic latitudes. The middle and end of the diagram correspond to the beginning of solar cycle 1, with sunspots at high latitudes ( 301). Note that at the end of the diagram, sunspots in both low and high latitudes are
Fig. 2. Six sunspot drawings published in the work De heliometri structura et usu by Zucconi (1760).
190
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
Sunspot Number
90 80
Group Sunspot Number
70
W olf Sunspot Number
60 50 40 30 20 10 0 40 30
Latitude
20 10 0 -10 -20 -30 -40 1753
1754
1755
1756
1757
1758
1759
1760
1761
Date Fig. 3. Sunspot number (January 1753–December 1761) and butterfly diagram based on the sunspot latitude estimations obtained from the Zucconi drawings (April 1754–June 1760).
present. In this regard, the diagram would be notably enhanced if a greater number of observations were available. However, there are many years with only sparse observations during the 18th century (Vaquero, 2007). In fact, Vaquero et al. (2007) speculated that the maximum value of cycle number 1 could have taken been place in 1760 and not in 1761.
4. Final words During the last 10 years, a great effort has been made to improve the time series of sunspot numbers from historical observations (Hoyt and Schatten, 1998; Vaquero, 2007). However, we must also incorporate historical information on solar activity into studies of the position of sunspots (differential rotation, active longitudes, north–south asymmetries, etc.). The HSUNSPOTS software (which is freely available to interested users) is a useful tool to estimate sunspot positions from early drawings. In this way, it can be employed to retrieve very interesting information that is still buried in archives and libraries around the world.
Acknowledgements This work was partially supported by the Ministerio de Ciencia e Innovacio´n of the Spanish Government (AYA2008-04864/AYA). The authors are in debt to David M. Willis who provided important comments that improved our initial manuscript.
References Arlt, R., 2008. Digitization of sunspot drawings by Staudacher in 1749–1796. Solar Physics 247, 399–410. Arlt, R., 2009. The butterfly diagram in the eighteenth century. Solar Physics 255, 143–153. Balthasar, H., Vazquez, M., Woehl, H., 1986. Differential rotation of sunspot groups in the period from 1874 through 1976 and changes of the rotation velocity within the solar cycle. Astronomy and Astrophysics 155, 87–98. ¨ Beck, R., Hilbrecht, H., Reinsch, K., Volker, P., 1995. Solar Astronomy Handbook. Willmann-Bell, Inc. Casas, R., Vaquero, J.M., Va´zquez, M., 2006. Solar rotation in the 17th century. Solar Physics 234, 379–392. Eddy, J.A., Gilman, P.A., Trotter, D.E., 1976. Solar rotation during the Maunder Minimum. Solar Physics 46, 3–14. Hoyt, D.V., Schatten, K.H., 1998. Group sunspot numbers: a new solar activity reconstruction. Solar Physics 179, 189–219 [Reprinted with figures in Solar Physics 181, 491, 1998]. Meeus, J., 1998. Astronomical Algorithms 2nd edition Willmann-Bell Inc. Phillips, K.J.H., 1992. Guide to the Sun. Cambridge University Press. Ribes, E., Ribes, J.C., Barthalot, R., 1987. Evidence for a larger sun with a slower rotation during the seventeenth century. Nature 326, 52–55. Roy, A.E., Clarke, D., 1989. Astronomy: Structure of the Universe. Adam Hilger. Royal Greenwich Observatory, 1980. Royal observatory annals. Photoheliographic Results 1972–1976, Royal Greenwich Observatory, Herstmonceux. Smart, W.M., 1977. Textbook on Spherical Astronomy 6th Ed. Cambridge University Press. Tobias, S.M., 2009. The solar dynamo: the role of penetration, rotation and shear on convective dynamos. Space Science Review 144, 77–86. Vaquero, J.M., Sa´nchez-Bajo, F., Gallego, M.C., 2002. A measure of the solar rotation during the Maunder Minimum. Solar Physics 207, 219–222. Vaquero, J.M., 2007. Historical sunspot observations: a review. Advances in Space Research 40, 929–941. Vaquero, J.M., Trigo, R.M., Gallego, M.C., Moreno-Corral, M.A., 2007. Two early sunspots observers: Teodoro de Almeida and Jose´ Antonio Alzate. Solar Physics 240, 165–175. Vaquero, J.M., Va´zquez, M., 2009. The Sun recorded through history: scientific data extracted from historical documents. Astrophysics and Space Science Library, vol. 361. Springer. Zucconi, L., 1760. De heliometri structura et usu, Venetiis.
Contents lists available at ScienceDirect
Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
HSUNSPOTS: A tool for the analysis of historical sunspot drawings A. Cristo a, J.M. Vaquero b,n, F. Sa´nchez-Bajo c a b c
´ceres, Spain Departamento de Tecnologı´a de los Computadores y de las Comunicaciones, Escuela Polite´cnica, Universidad de Extremadura, Avda de la Universidad s/n, 10071 Ca ´ceres, Spain Departamento de Fı´sica Aplicada, Escuela Polite´cnica, Universidad de Extremadura, Avda de la Universidad s/n, 10071 Ca Departamento de Fı´sica Aplicada, Escuela de Ingenierı´as Industriales, Universidad de Extremadura, Avda de Elvas s/n, 06071 Badajoz, Spain
a r t i c l e in fo
abstract
Article history: Accepted 28 December 2009 Available online 6 January 2010
Valuable information about the evolution of solar activity is recorded in early sunspot drawings, especially during 17th–19th centuries. In this context, we have developed a computer program to analyze historical drawings showing the trajectories of sunspots across the solar disk. As an example, we have analysed the drawings published in the book De heliometri structura et usu by Zucconi (1760). These drawings span the period from April 1754 to June 1760. We present the Butterfly diagram for those years. The ending of solar cycle 0 and the beginning of solar cycle 1 are clearly noted in this diagram. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Software Sunspots drawings 18th century data Butterfly diagram
1. Introduction Early drawings of sunspots (from the beginning of the 17th century) have been extensively used to characterize solar activity during past centuries, extending the series of sunspot numbers back into the past (Vaquero and Va´zquez, 2009). In this regard, studies of the solar activity based on the analysis of early sunspot observations are very important, owing to the intimate connection between the activity of the sun and the terrestrial climate. Moreover, these drawings can be also used to measure the position of sunspots and estimate the solar rotation rate by analyzing the changes in the position of the sunspots with time. In this regard, note that the only information on surface rotation during these centuries comes from contemporary drawings of the Sun including sunspots (Casas et al., 2006). In this way, note also that accurate and continuous records of the positions of the sunspots, used for determining the solar rotation rate, are only available for solar cycles since last decades of the 19th century (Royal Greenwich Observatory, 1980; Balthasar et al., 1986). The studies of solar rotation based on historical drawings of sunspots are important because of the link between solar activity and the solar dynamo (Tobias, 2009). In this regard, for example, some work has been performed using drawings from the so-called Maunder Minimum ( 1645 to 1715). Some of these studies suggest that solar rotation was more differential during the Maunder Minimum than at the present time (Eddy et al., 1976; Ribes et al., 1987; Vaquero et al., 2002). However, historical drawings useful for the measurement of solar rotation are sparse.
n
Corresponding author. Tel.: + 34 676 618 160; fax: + 34 924 289 651. E-mail addresses: [email protected] (A. Cristo), [email protected] (J.M. Vaquero), [email protected] (F. Sa´nchez-Bajo). 1364-6826/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2009.12.010
For this reason, the search and analysis of historical solar drawings to determine sunspot positions is an interesting task (Arlt, 2008, 2009). The analysis of ancient solar drawings can be performed manually, by measuring the number and positions of the identifiable sunspots on each drawing, one by one, and transforming subsequently these positions to heliographic coordinates by standard methods (Beck et al., 1995; Roy and Clarke, 1989; Smart, 1977). However, this is a tedious task that could be shortened by using an automatic procedure. For this reason, we present here HSUNSPOTS, a software tool developed for analyzing solar drawings, which can be employed in the study of ancient solar records. In the following sections we describe, first, the software, and, next, as an example, we use it to analyze the solar drawings prepared by Zucconi (1760).
2. Description of the software The program HSUNSPOTS is a windows-based computer tool especially developed to register, in an automatic way, the positions and areas of sunspots in solar drawings. It is intended for both historians of astronomy and solar physicists. This software has been developed over a C++ environment and runs under all Microsoft Windows platforms and will be available for GNU Linux operating systems soon. The low size of the application (about 1.2 MB) makes it very suitable for easy distribution. HSUNSPOTS is based on the creation of user projects, which store information (including contact information) about the observer or analyzer and the location of the place of the daily observations. For each project, a sequence of observations can be
188
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
Fig. 1. A sunspot drawing by Zucconi (upper panel) analysed with HSUNSPOTS software (lower panel).
managed by just loading an image of the Sun on the desired day and marking with a click of the mouse, in a very intuitive way, the sunspots present in the picture. The file storing a user project follows a structure designed for the application, and it is completely interchangeable. In this way, an observer can distribute his project file to others to consult his observations or to complete with the other observer’s data. In the near future, the application will be improved to be able to merge several users’ projects (in order to distribute the observation work among different authors), or to export read only projects, for a safer distribution and publication. It is possible to carry out several operations on the marked information, such as grouping the sunspots and labelling them to track the trajectory of these sunspots or groups over the solar disk; estimating the total sunspot area (which is related to solar activity); and showing the results in different kinds of charts. The application has been divided into four main windows.
template representing the state of the Sun (L0, B0, P angles and apparent diameter1). All the solar ephemeris information is firstly automatically calculated by transforming the observation date inserted by the user to the corresponding Julian Day, according to the expressions and tables detailed in Chapter 10 of Meeus (1998), and later using the Julian Day to automatically calculate the Sun’s L0, B0, P angles and apparent diameter according to the expressions detailed in the Chapter 29 of the same book. In this regard, we have adopted the convention of placing the east limb (E) to the right and the west limb (W) to the left, in opposite of the other convention used (Phillips, 1992). When all the ephemeris have been calculated and the user has placed the image over the template, then it is possible to select, with a mouse click, the sunspots visible in the drawing. In this regard, the measurement of data such as the position and relative area of the sunspots is carried out in an automatic way by the program (using the auxiliary data L0, B0 and P for the date of the observation, previously calculated) and stored for use in subsequent windows.
2.1. Analysis window This is the main option window (Fig. 1). It allows the user to load an image of the Sun, move it, rotate it, resize it and/or change its opacity in order to adjust the solar limb to a predefined
1 L0 and B0 are, respectively, the heliographic longitude and latitude of the centre of the solar disk. P is the position angle of the northern extremity of the axis of rotation, measured eastwards from the North Point of the solar disk.
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
2.2. Viewing/editing window This window allows the user to display the data of the groups and sunspots analysed in the previous window (heliographic coordinates, relative areas and hemisphere where they are located), and edit them. The groups and spots analysed are also shown graphically in this window. 2.3. Tracking window In this window, the labelled groups and sunspots are displayed in order to analyze their temporal behaviour and their trajectories over the solar disk. 2.4. Statistics window In this window it is possible, using various charts, to display different parameters of the labelled data, such as the total area or number (by hemisphere, if required) of the groups and sunspots, along with the time period of the observations.
3. An example: Zucconi’s drawings A set of early sunspot drawings was published by Zucconi (1760), showing the path across the solar disk of some spots observed
189
during the period from April 1754–June 1760. Fig. 2 shows, as an example, six sunspot drawings published by Zucconi (1760) although the complete set includes 38 drawings. Information about a precise date and time for all the drawings is provided by Zucconi (1760). HSUNSPOTS was used to estimate the position of all the recorded sunspots (1202 in total, involving about 60 sunspot groups) on different observation days. In these drawings, the sunspots show fine details, although the quality of the alignment of the sunspots and the cardinal directions is not ideal. It is possible to see, the E/W coordinates of the Sun’s limb are the opposite in the application regarding the Zucconi’s drawings. Because of this, it was necessary to flip all the drawings horizontally before analyzing them with the program. In the next version advanced image transformations will be available, such as horizontal and vertical flipping and rotation. After analyzing the flipped Zucconi’s drawings, using the estimated sunspot positions calculated automatically by the application, a Butterfly diagram (Fig. 3, lower panel) that spans the period 1754–1760 has been generated. We have included both Wolf and Group Sunspot Number in Fig. 3 (upper panel). Butterfly diagram is compatible with the actual (and poor) knowledge of solar activity during these years. At the beginning of the diagram, where the number of observations is higher, the ending of solar cycle 0 is noticeable, with sunspots located at very low heliographic latitudes. The middle and end of the diagram correspond to the beginning of solar cycle 1, with sunspots at high latitudes ( 301). Note that at the end of the diagram, sunspots in both low and high latitudes are
Fig. 2. Six sunspot drawings published in the work De heliometri structura et usu by Zucconi (1760).
190
A. Cristo et al. / Journal of Atmospheric and Solar-Terrestrial Physics 73 (2011) 187–190
Sunspot Number
90 80
Group Sunspot Number
70
W olf Sunspot Number
60 50 40 30 20 10 0 40 30
Latitude
20 10 0 -10 -20 -30 -40 1753
1754
1755
1756
1757
1758
1759
1760
1761
Date Fig. 3. Sunspot number (January 1753–December 1761) and butterfly diagram based on the sunspot latitude estimations obtained from the Zucconi drawings (April 1754–June 1760).
present. In this regard, the diagram would be notably enhanced if a greater number of observations were available. However, there are many years with only sparse observations during the 18th century (Vaquero, 2007). In fact, Vaquero et al. (2007) speculated that the maximum value of cycle number 1 could have taken been place in 1760 and not in 1761.
4. Final words During the last 10 years, a great effort has been made to improve the time series of sunspot numbers from historical observations (Hoyt and Schatten, 1998; Vaquero, 2007). However, we must also incorporate historical information on solar activity into studies of the position of sunspots (differential rotation, active longitudes, north–south asymmetries, etc.). The HSUNSPOTS software (which is freely available to interested users) is a useful tool to estimate sunspot positions from early drawings. In this way, it can be employed to retrieve very interesting information that is still buried in archives and libraries around the world.
Acknowledgements This work was partially supported by the Ministerio de Ciencia e Innovacio´n of the Spanish Government (AYA2008-04864/AYA). The authors are in debt to David M. Willis who provided important comments that improved our initial manuscript.
References Arlt, R., 2008. Digitization of sunspot drawings by Staudacher in 1749–1796. Solar Physics 247, 399–410. Arlt, R., 2009. The butterfly diagram in the eighteenth century. Solar Physics 255, 143–153. Balthasar, H., Vazquez, M., Woehl, H., 1986. Differential rotation of sunspot groups in the period from 1874 through 1976 and changes of the rotation velocity within the solar cycle. Astronomy and Astrophysics 155, 87–98. ¨ Beck, R., Hilbrecht, H., Reinsch, K., Volker, P., 1995. Solar Astronomy Handbook. Willmann-Bell, Inc. Casas, R., Vaquero, J.M., Va´zquez, M., 2006. Solar rotation in the 17th century. Solar Physics 234, 379–392. Eddy, J.A., Gilman, P.A., Trotter, D.E., 1976. Solar rotation during the Maunder Minimum. Solar Physics 46, 3–14. Hoyt, D.V., Schatten, K.H., 1998. Group sunspot numbers: a new solar activity reconstruction. Solar Physics 179, 189–219 [Reprinted with figures in Solar Physics 181, 491, 1998]. Meeus, J., 1998. Astronomical Algorithms 2nd edition Willmann-Bell Inc. Phillips, K.J.H., 1992. Guide to the Sun. Cambridge University Press. Ribes, E., Ribes, J.C., Barthalot, R., 1987. Evidence for a larger sun with a slower rotation during the seventeenth century. Nature 326, 52–55. Roy, A.E., Clarke, D., 1989. Astronomy: Structure of the Universe. Adam Hilger. Royal Greenwich Observatory, 1980. Royal observatory annals. Photoheliographic Results 1972–1976, Royal Greenwich Observatory, Herstmonceux. Smart, W.M., 1977. Textbook on Spherical Astronomy 6th Ed. Cambridge University Press. Tobias, S.M., 2009. The solar dynamo: the role of penetration, rotation and shear on convective dynamos. Space Science Review 144, 77–86. Vaquero, J.M., Sa´nchez-Bajo, F., Gallego, M.C., 2002. A measure of the solar rotation during the Maunder Minimum. Solar Physics 207, 219–222. Vaquero, J.M., 2007. Historical sunspot observations: a review. Advances in Space Research 40, 929–941. Vaquero, J.M., Trigo, R.M., Gallego, M.C., Moreno-Corral, M.A., 2007. Two early sunspots observers: Teodoro de Almeida and Jose´ Antonio Alzate. Solar Physics 240, 165–175. Vaquero, J.M., Va´zquez, M., 2009. The Sun recorded through history: scientific data extracted from historical documents. Astrophysics and Space Science Library, vol. 361. Springer. Zucconi, L., 1760. De heliometri structura et usu, Venetiis.