Question: Under which Roman Emperor's effective conquest of Britain was it possible that Jews visited Scotland?

Context articles: History of the Jews in Scotland
Alexandria riot (66)
Marcia Servilia Sorana
Roman conquest of Britain
Antonia Gordiana
Vibia Aurelia Sabina
Louis II of Italy
Britannia
Australian cricket team in Scotland in 2013
Fadilla

The earliest date at which Jews arrived in Scotland is not known.
 It is possible that Jews visited Scotland at the time of the Roman Empire's conquest of southern Britain, but there are no records of this.
 The earliest concrete historical references to Jews in Scotland are from the late 17th century.
 The vast majority of Scottish Jews today are Ashkenazi who mainly settled in Edinburgh, then in Glasgow in the mid 19th century.
 Most histories of Jews in Scotland deal with the subject from a British perspective, thus tending to marginalise any distinctly Scottish dimension.
Extensive riots erupted in Alexandria, Roman Egypt, in 66 CE, in parallel with the outbreak of the First Jewish–Roman War in neighbouring Roman Judea.
 With the rising tension between the Greeks and the Jews the Alexandrines had organized a public assembly to deliberate about an embassy to Nero, and a great number of Jews came flocking to the amphitheater.
 When the Alexandrines saw the Jews they attacked them.
 They killed the majority of the Jews and those who were captured were burned alive.
 The Jews wanted retaliation for what the Greeks had done and threatened to do it with violence.
 However, Tiberius Julius Alexander, the governor of the city, was able to restrain them.
 Tiberius privately sent for the principal men of the Jews, and convinced them to be quiet, and not provoke the Roman army against them.
 But the seditious did not take the threat seriously, and reproached him for so uttering threats.
 The governor now understood that those who were most riotous would not be pacified unless some great calamity would overtake them.
 He sent out the two Roman legions that were in the city (the Third Legion Cyrenaica and the Twenty-Second Deiotariana), together with 5,000 other soldiers, to punish the Jews.
 They were permitted not only to kill them, but to plunder them of what they had, and to set fire to their houses.
 The Romans showed no mercy to the infants, had no regard for the aged, and went on in the slaughter of persons of every age; over 50,000 Jews lay dead in the streets.
 Tiberius Julius Alexander eventually took mercy on the Jews and called off the attacks.
 This was one riot of many that broke out in not only Alexandria, but also in Damascus, Caesarea and in many other places.
 During the events, the prefect Iulius Alexander attacked the Jewish quarter of the city.
Marcia Servilia Sorana or commonly known as Servilia (40s-66) was the daughter of Roman Senator Quintus Marcius Barea Soranus and her mother may have been from the gens Servilia.
 Servilia's paternal uncle was the Roman Senator Quintus Marcius Barea Sura, who was a friend to the future Roman Emperor Vespasian.
 Her paternal cousins were Marcia (mother of Ulpia Marciana and of future Roman Emperor Trajan) and Marcia Furnilla (the second wife of the future Roman Emperor Titus).
 Her paternal grandfather Quintus Marcius Barea Soranus was Suffect Consul in 34 and twice Proconsul of Africa.
The Roman conquest of Britain was a gradual process, beginning effectively in AD 43 under Emperor Claudius, whose general Aulus Plautius served as first governor of Roman Britain (Latin: "Britannia" ).
 Great Britain had already frequently been the target of invasions, planned and actual, by forces of the Roman Republic and Roman Empire.
 In common with other regions on the edge of the empire, Britain had enjoyed diplomatic and trading links with the Romans in the century since Julius Caesar's expeditions in 55 and 54 BC, and Roman economic and cultural influence was a significant part of the British late pre-Roman Iron Age, especially in the south.
Antonia Gordiana (201 - ?)
 was a prominent, wealthy and noble Roman woman who lived in the troubled and unstable 3rd century.
 She was the daughter of Roman Emperor Gordian I; sister to Roman Emperor Gordian II and mother to Roman Emperor Gordian III.
 Gordiana’s mother may be the granddaughter of Greek Sophist, consul and tutor Herodes Atticus.
Vibia Aurelia Sabina (170 AD – before 217 AD) was a Roman Princess.
 She was the youngest daughter and child born to Roman Emperor Marcus Aurelius and Roman Empress Faustina the Younger.
 She was a sister to Roman Empress Lucilla and Roman Emperor Commodus.
 Her maternal grandparents were Roman Emperor Antoninus Pius and Roman Empress Faustina the Elder and her paternal grandparents were Domitia Lucilla and praetor Marcus Annius Verus.
Louis II, sometimes called the Younger (825 – 12 August 875), was the King of Italy and Holy Roman Emperor from 844, co-ruling with his father Lothair I until 855, after which he ruled alone.
 Louis's usual title was "imperator augustus" ("august emperor"), but he used "imperator Romanorum" ("emperor of the Romans") after his conquest of Bari in 871, which led to poor relations with the Eastern Roman Empire.
 He was called "imperator Italiae" ("emperor of Italy") in West Francia while the Byzantines called him "Basileus Phrangias" ("Emperor of the Franks").
 The chronicler Andreas of Bergamo, who is the main source for Louis's activities in southern Italy, notes that "after his death a great tribulation came to Italy."
Britannia was a Roman-Britain province inhabited by the Celtic Britons, Belgae and Picts, encompassing parts of the island south of Caledonia (roughly Scotland) of the geographical region of Great Britain and is the name given to the female personification of the island.
 It is a term still used to refer to the island.
 The name is Latin, and derives from the Greek form "Prettanike" or "Brettaniai", which originally designated a collection of islands with individual names, including "Albion" or Great Britain.
 By the 1st century BC, "Britannia" came to be used for Great Britain specifically.
 The Romans had initially called the entire provincial island "Britain" and it was only when the island was split into four provinces that two were given the name "Britannia".
 Although Britain had been designated part of the Roman Empire in 43 AD during the conquest of emperor Claudius it wasn't until the end of the 2nd century that Britannia had been pacified and fully adopted Roman practices.
The Australia cricket team visited Scotland on 3 September 2013 for a one-match One Day International series against the Scotland cricket team at Grange Cricket Club Ground, Raeburn Place, Edinburgh.
 The match will serve as a warm-up for Australia ahead of their five-match ODI series against England later in the month.
 Australia won the match by 200 runs.
Annia Aurelia Fadilla, most commonly known as Fadilla (159-died after 211) was an influential Roman Princess and was one of the daughters born to Roman Emperor Marcus Aurelius and Roman Empress Faustina the Younger.
 She was a sister to Roman Empress Lucilla and Roman Emperor Commodus.
 Fadilla was named in honor of her late maternal aunt Aurelia Fadilla.
 The cognomen Fadilla, was the cognomen of the mother and a half-sister of the previous Roman Emperor Antoninus Pius.
 Her maternal grandparents were Roman Emperor Antoninus Pius and Roman Empress Faustina the Elder and her paternal grandparents were Domitia Lucilla and praetor Marcus Annius Verus.