Question: Bilawal is a raga and basic "thaat" (musical mode) in Hindustani classical music, it is equivalent to which rāga in Carnatic music?
Context: Dhīraśankarābharaṇaṃ, commonly known as "Śankarābharaṇaṃ", is a rāga in Carnatic music.  It is the 29th "Melakarta" rāga in the 72 "Melakarta" rāga system of Carnatic music.  Since this raga has many Gamakās (ornamentations), it is glorified as ""Sarva Gamaka Maṇika Rakti Rāgaṃ"" in Telugu. Raga Jaijaivanti also spelled as "Jaijaiwanti" is a rāga in Hindustani classical music in Khamaj thaat.  According to the Guru Granth Sahib, this raga is a mixture of two other ragas - Bilaval and Sorath.  This raga has not been mentioned in any ancient Indian classical scriptures on music.  It is also not mentioned in the Ragmala at the end of Granth Sahib. Bilawal is a raga and basic "thaat" (musical mode) in Hindustani classical music.  It is equivalent to the Carnatic melakarta raga Dheerasankarabharanam, as well as the Western Ionian mode (major scale) and contains the notes S R G m P D N S' ("see swara for explanation").  The pitches of Bilawal thaat are all shuddha, or natural.  Flat (komal) or sharp (tivra) of pitches always occurs with reference to the interval pattern in Bilawal thaat.  The Indian national anthem  Jana gana mana is sung in raag Bilawal. Vatapi Ganapatim, also known as Vatapi ganapatim bhaje ham or Vatapi ganapatim bhaje, is a Sanskrit "kriti" song by the South Indian poet-composer Muthuswami Dikshitar (1775–1835), one of the "Trinity of Carnatic music".  The panegyrical hymn praises Vatapi Ganapati, Ganesha (Ganapati) worshipped in a shrine in Tiruchenkattankudi in the Indian state of Tamil Nadu.  The hymn is composed in Hamsadhvani raga (musical mode), however in tradition of kritis, individual performers add their own variations in the tune.  "Vatapi Ganapatim" is described as the best-known piece of Muthuswami Dikshitar as well as one of the most popular compositions of Carnatic music (South Indian classical music school).  The hymn is traditionally sung at the beginning of many Carnatic music concerts. Raga Jaunpuri , Jonpuri, or Javanpuri is a rāga in Hindustani classical music in the Asavari thaat.  Some experts like Pandit Omkarnath Thakur consider it indistinguishable from the shuddha rishabh Asavari.  Its attractive swaras also make it a popular raga in the Carnatic circles with a number of compositions in South India being tuned to Jonpuri. Madhyamavati (madhyamāvati) is a rāga in Carnatic music (musical scale of South Indian classical music).  It is an "audava" rāga (or "owdava" rāga, meaning pentatonic scale).  It is a "janya" rāga (derived scale), as it does not have all the seven musical notes ("swaras").  The equivalent of "Madhyamavati" in Hindustani music is "Madhumad Sarang". Shubhapantuvarali (pronounced śubhapantuvarāḻi , meaning "the auspicious moon") is a rāgam in Carnatic music (musical scale of South Indian classical music).  It is the 45th "melakarta" rāgam in the 72 "melakarta" rāgam system of Carnatic music.  It is called Shivapantuvarāḻi in Muthuswami Dikshitar school of Carnatic music.  Todi (thaat) is the equivalent in Hindustani music. Mohanam is a rāga in Carnatic music (musical scale of South Indian classical music).  It is an "audava" rāga (or "owdava" rāga, meaning pentatonic scale).  It is a "janya" rāga of Harikambojhi(28th Melakartha Raga).  However there are disputes about Mohanam being the janya of Sankharbharanam also because all the swaras present in the Arohana and Avarohana of Mohanam satisfy both the melakartha ragas listed above. Alhaiya Bilaval is a Hindustani classical raga.  It is the most commonly performed raga of a large group of ragas that are mainly based on a scale more or less identical to the western major scale.  For this reason, that scale itself is known as the Bilaval "Thaat".  It is often simply referred to as Bilawal, although in the 17th century Alhaiya and Bilawal may have been separate ragas.  Alhaiya Bilawal is a raag which M is the main key. Kharaharapriya is a rāga in Carnatic music.  It is the 22nd "melakarta" rāga (parent scale) in the 72 "melakarta" rāga system.  It is possible that the name of the ragam was originally "Harapriya" but it was changed to conform to the Katapayadi formula.  "Kharaharapriya" has a distinct melody and brings out the "Karuna" rasam, invoking pathos in the listeners.  The "Kafi thaat" of Hindustani music is the equivalent of "Kharaharapriya".
Answer: Dheerasankarabharanam